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# Indian Journal of Advanced Mathematics (IJAM): The IJAM aims to publish high-quality, peer-reviewed original articles in Mathematics.

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- [Journal Metrics](https://www.ijam.latticescipub.com/journal-metrics/): Journal Metrics:
- [Article Submission System](https://www.ijam.latticescipub.com/article-submission-system/): If there is any problem in uploading the article through the form given below, the author can also email the article to support@latticescipub.com with the following details: Your name, Mobile No, WhatsApp No, Country Name, Email, Other email (optional), Scope of the article, Author(s) Name (Min-01, Max 05), Title of the Article, Name of the journal.
- [Archiving](https://www.ijam.latticescipub.com/archiving-policy/): Archiving:
- [Imprint](https://www.ijam.latticescipub.com/imprint/): Full Journal Title: Indian Journal of Advanced Mathematics (IJAM) ISSN: 2582-8932 (Online) Publisher: Lattice Science Publication (LSP) Publisher Location: India. Postal Address: Lattice Science Publication (LSP), # G-20, Block-A, Tirupati Abhinav Commercial Campus, Tirupati Abhinav Homes, Ayodhya Bypass Road, Damkheda, Bhopal (Madhya Pradesh)-462037, India. Editors: Editorial Board Publication Frequency: Half Yearly Publication Medium: Online (Electronic Only) Publication Website: www.ijam.latticescipub.com First Year Published: 2021 Indexing Databases: Indexing & Abstracting Journal DOI: https://doi.org/10.54105/ijam Publication Language: English Primary Field: Mathematics Archive: https://www.ijam.latticescipub.com/archive/ CrossRef: Yes Guidelines for Authors: https://www.ijam.latticescipub.com/instruction-for-authors/ Editorial and Publishing Policies: https://www.ijam.latticescipub.com/ethics-policies/ Publisher License under: CC-BY-NC-ND 4.0
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- [Published in Year 2023](https://www.ijam.latticescipub.com/published-in-year-2023/)
- [Important Dates](https://www.ijam.latticescipub.com/dates/): Authors can electronically submit articles throughout the year using the Article Submission System. Authors can format their article either in (i) a single-column format or (ii) as per the journal template. The submitted articles should not have been previously published or are currently under consideration for publication elsewhere. The journal does not accept brief or short notes for publication. The editors retain the right to reject any articles that lack quality or originality without sending them for review. All articles must fall within the journal's scope and will undergo a double-anonymized peer-review process. Authors must confirm that they have read and understood the content of their submitted article and ensure that it meets acceptable English grammar and usage standards. To help with the proofreading process, authors can use tools like Grammarly or similar applications. As an open-access journal, authors must pay an Article Processing Charge (APC) to publish their articles and retain copyright. Additionally, authors should familiarise themselves with the editorial and publishing policies of the journal.
- [Published in Year 2022](https://www.ijam.latticescipub.com/published-in-year-2022/)
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- [Indexing and Abstracting](https://www.ijam.latticescipub.com/indexing/): It is crucial to comprehend that the decision to add an article to an indexing and abstracting database, such as Scopus, is solely made by the team and not the Indian Journal of Advanced Mathematics (IJAM). Therefore, the Indian Journal of Advanced Mathematics (IJAM) has no authority over whether an article is accepted or rejected for inclusion in the database. Furthermore, the Indian Journal of Advanced Mathematics (IJAM) does not affect the required processing time of an article for inclusion in the indexing and abstracting database. The indexing and abstracting details of the journal are given below:
- [Published in Year 2021](https://www.ijam.latticescipub.com/published-in-year-2021/)
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- [Guidelines for Authors](https://www.ijam.latticescipub.com/instruction-for-authors/): Guidelines for Authors:
- [HOME](https://www.ijam.latticescipub.com/): The IJAM aims to publish high-quality, peer-reviewed original articles in Mathematics.
- [Editorial and Publishing Policies](https://www.ijam.latticescipub.com/ethics-policies/): Editorial and Publishing Policies:
- [EDITORIAL BOARD](https://www.ijam.latticescipub.com/editorial-board/): Editor-In-Chief
- [DOWNLOAD](https://www.ijam.latticescipub.com/download/): Authors can download following items as per their requirements:
- [Intellectual Property](https://www.ijam.latticescipub.com/copyright-grants-and-ownership-declaration/): These permissions are granted under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) License. The Indian Journal of Advanced Mathematics (IJAM) encourage users to share and disseminate the work, providing appropriate credit to the original authors and refraining from altering or using the content commercially. This inclusive approach allows a broader audience to benefit from shared knowledge.
- [CONTACT](https://www.ijam.latticescipub.com/contact/): The author can submit the below form for any query. Each query will be resolved within 72 hours.
- [CALL FOR PAPERS](https://www.ijam.latticescipub.com/call-for-papers/): Dear Professor, | Scientist | Scholar, You are invited to submit original research articles as per your research expertise. Articles can be submitted from the journal website by using the ‘Article Submission System’ throughout the year if: Plagiarism of the article is less than 15%, including references. The article is within the scope of the journal. The article is original and result-oriented. For more detailed information, please visit ‘Guidelines for Authors’.  Important Dates-  Articles Submission Open for Volume-6 Issue-2, October 2026  Last Date of Article Submission: 30 September 2026 Date of Notification: 15 October 2026 Date of Publication: 30 October 2026
- [Article Processing Charge (APC)](https://www.ijam.latticescipub.com/article-processing-charge-apc-policy/): Authors must pay a fixed APC to publish their articles in the journal to retain copyright. The APC is payable only upon acceptance, not before or upon rejection.
- [ARCHIVE](https://www.ijam.latticescipub.com/archive/): The Indian Journal of Advanced Mathematics (IJAM) publish two types of issues: (1) Regular Issues and (2) Theme-Based Special Issues (announced from time to time). The Authors may submit articles electronically throughout the year using the Article Submission System. After the final acceptance of the article, based upon the detailed review process, the article will immediately be published online. For Theme-Based Special Issues, time-bound special calls for articles will be announced. Authors are allowed to download published articles. The articles published in the Indian Journal of Advanced Mathematics (IJAM) are open-access and accessible online without subscription fees as soon as it is published.
- [AIM AND SCOPE](https://www.ijam.latticescipub.com/aims-and-scope/): IJAM is a comprehensive platform dedicated to fostering a harmonious convergence between theoretical research, industry best practices, and cutting-edge concepts across various realms of Mathematics.

## Downloads
- [Volume-6 Issue-1, April 2026](https://www.ijam.latticescipub.com/download/volume-6-issue-1/): Editor-In-Chief
- [Volume-5 Issue-2, October 2025](https://www.ijam.latticescipub.com/download/volume-5-issue-2/): Editor-In-Chief
- [Volume-5 Issue-1, April 2025](https://www.ijam.latticescipub.com/download/volume-5-issue-1/): Editor-In-Chief
- [Volume-4 Issue-2, October 2024](https://www.ijam.latticescipub.com/download/volume-4-issue-2/): Editor-In-Chief
- [Volume-4 Issue-1, April 2024](https://www.ijam.latticescipub.com/download/volume-4-issue-1/): Editor-In-Chief
- [Volume-3 Issue-2, October 2023](https://www.ijam.latticescipub.com/download/volume-3-issue-2/): Editor-In-Chief
- [Volume-3 Issue-1, April 2023](https://www.ijam.latticescipub.com/download/volume-3-issue-1/): Editor-In-Chief
- [Volume-2 Issue-2, October 2022](https://www.ijam.latticescipub.com/download/volume-2-issue-2/): Editor-In-Chief
- [Volume-2 Issue-1, April 2022](https://www.ijam.latticescipub.com/download/volume-2-issue-1/): Editor-In-Chief
- [Volume-1 Issue-2,October 2021](https://www.ijam.latticescipub.com/download/volume-1-issue-2/): Editor-In-Chief
- [Volume-1 Issue-1, April 2021](https://www.ijam.latticescipub.com/download/volume-1-issue-1/): Editor-In-Chief

## Portfolio Items
- [B120405021025](https://www.ijam.latticescipub.com/portfolio-item/b120405021025/): This paper presents the first complete and definitive disproof of Goldbach’s Conjecture, executed through a synthesis of deep mathematical insight, theoretical innovation, and structural rigour. Across a broad spectrum of modern mathematics, this work reveals foundational contradictions that undermine the conjecture’s claim to universality. The result is a clear and categorical conclusion that Goldbach’s Conjecture, while numerically resilient, collapses under formal scrutiny. This work not only resolves a centuries-old enigma but redefines the philosophical foundation of additive number theory. It proactively challenges the mathematical community to distinguish between empirical tradition and provable truth, and sets a new standard for resolving longstanding conjectures. In doing so, it transforms the landscape of number theory and establishes a model for multidisciplinary proof that enables future breakthroughs. This is not merely a mathematical achievement but a historic turning point as the era of Goldbach concludes, and the era of mathematical evolution begins.
- [B120305021025](https://www.ijam.latticescipub.com/portfolio-item/b120305021025/): For over 160 years, the Riemann Hypothesis has stood as a cornerstone of modern mathematics: profound, elegant, and elusive. Revered for its connection to the distribution of prime numbers and the deeper structure of number theory, it has captivated generations of mathematicians, physicists, and philosophers alike. Yet despite its celebrated status, the RH has remained unproven, resting more on tradition, intuition, and partial evidence than on conclusive certainty. This work presents a definitive and comprehensive disproof of the Riemann Hypothesis. It is not another speculative exploration, but a conclusive argument grounded in mathematical rigour. Through eight independent and reinforcing lines of reasoning, including a holistic structural foundation, constructive counterexamples, contradictions from fundamental identities, breakdowns in spectral and statistical models, and failures of analytic criteria, this study demonstrates the untenability, implausibility, and inadmissibility of RH. Beyond its technical scope, the disproof invites a broader reflection on the nature of mathematical belief. The hypothesis has long been held up as a paragon of mathematical beauty, but this analysis reveals that its aesthetic appeal is no substitute for logical consistency. Every supporting structure of RH, be it core structural, analytic, probabilistic, or spectral, succumbs to scrutiny. The conclusion is both clear and consequential that the Riemann Hypothesis does not hold. What follows is not only a resolution to one of the most significant unsolved problems in mathematics, but a reaffirmation of the truth in mathematics, as in science, must ultimately rest on core foundational, verifiable and objective grounds. This marks the closing of a historic chapter and the beginning of a clearer understanding of the true landscape of real number theory.
- [A124406010426](https://www.ijam.latticescipub.com/portfolio-item/a124406010426/): In this paper, we explain the logic for simultaneously solving linear congruences using the Chinese Remainder Theorem and apply it to develop an easy method for finding the solution. Mathematics Subject Classification : Primary 11A41.
- [A124206010426](https://www.ijam.latticescipub.com/portfolio-item/a124206010426/): Let 𝑨 denote the multiplicative group {𝟏,−𝟏,𝒊, −𝒊}. In this paper, we define the notion of double uniform (𝑡1𝑙1,𝑡2𝑙2)-ply and prove that it is a group 𝑨-cordial with each path of length at least 5 by explicitly giving labellings for all the possible cases that arise. Mathematics Subject Classification : Primary 05C78
- [A124106010426](https://www.ijam.latticescipub.com/portfolio-item/a124106010426/): In this paper, I investigate the method for constructing Maximum Distance Separable (MDS) codes using exponential sums. By utilizing the properties of the trace function over finite fields, I explicitly calculate linear codes associated with certain three-term exponential sums. The parameters, weight distributions, and distance properties of these codes are analyzed in detail. Furthermore, we analyse the syndrome-decoding process for these codes.
- [A123906010426](https://www.ijam.latticescipub.com/portfolio-item/a123906010426/): This paper presents a straightforward and elementary proof of Fermat’s Last Theorem (FLT), asserting that there are no integer solutions to 𝒂 𝒏 + 𝒃 𝒏 = 𝒄 𝒏 for 𝒏 > 𝟐. Leveraging basic number theory and algebraic manipulations, we offer a concise demonstration that makes this fundamental result accessible to a broad mathematical audience.
- [A123606010426](https://www.ijam.latticescipub.com/portfolio-item/a123606010426/): Many foundational rules in elementary and advanced mathematics are accepted as axiomatic, despite being introduced through heuristic or pedagogical arguments rather than strict logical or physical justification. This work undertakes a systematic analytical re-examination of several such widely accepted mathematical conventions to identify internal inconsistencies and clarify their conceptual basis. The study begins by reanalysing the four basic arithmetic operations—addition, subtraction, multiplication, and division—by reducing multiplication and division to repeated addition and subtraction. Within this framework, the conventional sign rules governing the multiplication of negative quantities are critically examined. It is shown that while the outcomes of these rules are operationally consistent, the standard logical justifications commonly provided are incomplete or internally inconsistent when interpreted in terms of direction, orientation, and repetition. Using geometric constructions and physically motivated examples, the work further examines the interpretation of signed quantities, demonstrating that positive and negative values naturally encode directionality rather than intrinsic magnitude. This perspective is extended to areas and volumes, which are typically assumed to be strictly non-negative. The analysis shows that signed areas and volumes can be meaningfully interpreted within a consistent mathematical–physical framework, thereby questioning one of the key assumptions underlying the introduction of imaginary quantities. The paper also revisits the treatment of fractional quantities, squaring operations, and dimensional comparisons, arguing that several commonly cited “paradoxes” arise from conflating quantities of different dimensions or from scaledependent representations rather than from inherent mathematical necessity. Additionally, division by zero and infinity is reinterpreted through the lens of repeated subtraction, yielding a physically intuitive understanding of divergence and null results. Finally, the exponential function and its Taylor series expansion are examined from combinatorial and geometric perspectives, offering an alternative interpretation of the exponential constant based on dimensional arrangements rather than abstract growth alone. Overall, this work does not seek to discard established mathematical tools, but to clarify their conceptual foundations by enforcing consistency across arithmetic, geometry, and physical interpretation. The results highlight the need for greater precision in distinguishing operational rules from their underlying logical and physical meanings.
- [A123406010426](https://www.ijam.latticescipub.com/portfolio-item/a123406010426/): Jensen’s inequality is a fundamental result in probability and analysis, that offers simple boundsforthe convex function applied to a random variable. However, the classical form of this process does not include memory effects, which are very important in some physical and financial systems with long-range dependence. In this paper, we introduce a fractional-order generalisation of Jensen’s inequality involving memory effects that can be accounted for by means of fractional calculus. We concentrate on the exponential integral function Ei(x) because of its wide use. For a random variable Xwith mean µsupported on − M(α), where the new quantity M(α) is a memory correction defined in terms of Riemann– Liouville fractional integrals of order 1 − αof the function e t /t. The correction term provides a whole family of bounds, controlled by the parameter α ∈ (0, 1], and depending on the specific behavior of X, as α→ 0+ , the bound reduces to Jensen’s gap, while for α → 1 —, the right-hand side approaches a new non-zero and pathdependent bound. The inequality is strict for non-degenerate X. (When M(α) ≥ 0, the bound is two-sided, Ei(µ) ≤ E − M(α) ≤ E.) The proof is based on order-monotonicity properties of fractional integrals. An equivalent formulation of the result in terms of Caputo derivatives is also given. An illustrative interpretation is discussed in the context of economic utility, where the resulting bounds may be viewed as capturing nonlocal averaging effects in convex (risk-seeking) utility evaluations.
- [A123306010426](https://www.ijam.latticescipub.com/portfolio-item/a123306010426/): In this paper, we show that a non-trivial zero of the Riemann zeta function occurs only when the complex number s = 𝒂/𝒃 + it, with 𝒂, 𝒃, 𝒕 ∈ 𝑹 and i² = -1 can be interpreted as a vector plus its inverse yielding zero displacement. We prove that for such a zero displacement to occur, the total distance covered by the vector and itsinverse must equal one unit, forcing the fundamental part of s to be 𝟏 𝟐 . We further show that no other fraction in the critical strip possesses this property. Consequently, no other fundamental part can host non-trivial zeros, thereby settling the Riemann Hypothesis.
- [A123106010426](https://www.ijam.latticescipub.com/portfolio-item/a123106010426/): I will study the Sghiar’s function Ⓢ:(X,z)⟼∏_(p∈P)1/(1-X/p^z ), P the set of prime numbers. Which is an extension of the Riemann zeta function. The classical form of the Riemann zeta function and its Euler product are well known in analytic number theory, and I will show that : ζ(s)=0 and Re(s)>1/2⇒Ⓢ=0. We deduce the proof of the Riemann Hypothesis. MSC code: 11M26 ; 97F60 ; 32A10
- [A123006010426](https://www.ijam.latticescipub.com/portfolio-item/a123006010426/): Goldfeld conjectured: “a positive proportion of quadratic twists of an elliptic curve E/Q have an analytic rank of 1. In this work, we confirm this assertion for infinitely many elliptic curves.
- [A122806010426](https://www.ijam.latticescipub.com/portfolio-item/a122806010426/): This paper investigates the arithmetic structure of exponential Diophantine equations of the form A x + B y= k n , where A, B, k, x, y, n ∈ Z + . Classical treatments such as the Beal Conjecture and Fermat’s Last Theorem (FLT) restrict attention to exponents greater than two, leaving open the structural behavior of the equation for n = 1 and n = 2. This manuscript provides a unified framework addressing all positive integer exponents. A central theorem establishes that each term A x, B y, and k n can be expressed as the sum of an arithmetic sequence whose number of terms and average term are positive integers, provided the equation has a trivial or non-trivial common factor. This elasticity property of k n is derived through Gauss’s method for summing arithmetic progressions. The case n = 2 recovers the classical identity for k 2 as the sum of the first k odd integers, revealing Pythagoras’ theorem as a special instance of the general framework. For exponents exceeding two, if gcd(A, B,k) = 1, the arithmetic structure collapses, aligning with the Beal Conjecture as it is presented in the literature as a generalization of FLT. The results demonstrate a consistent theory for all positive integer exponents and show that every sum of two positive integers has either a trivial or a non-trivial common factor.
- [A122606010426](https://www.ijam.latticescipub.com/portfolio-item/a122606010426/): This paper presents a general formula for calculating a player’s probability of winning in a sequential, turn-based game with a constant success probability per trial. The problem extends the classical two-player probability models of dice tossing or coin flipping to an arbitrary number of n players. A compact proof based on the summation of a geometric series is provided, and examples demonstrate the correctness and applicability of the result. This formulation can serve as an educational tool for understanding probabilistic reasoning, sequences, and infinite series.
- [A123806010424](https://www.ijam.latticescipub.com/portfolio-item/a123806010424/): This paper investigates the approximation of functions by Legendre wavelet expansions when their first and second derivatives belong to the generalized Lipschitz class Lip(𝛼, 𝑝), 0 < 𝛼 ≤ 1. Explicit error bounds are obtained in the 𝐿 2 -norm, showing that the rate of convergence depends on both the resolution level and the polynomial degree of the wavelet basis. The analysis reveals that Legendre wavelet estimators achieve sharper approximation orders than classical Fourier series and Haar wavelet methods under comparable smoothness assumptions. These results extend earlier studies on Lipschitz-type approximation and highlight the effectiveness of Legendre wavelets for functions with higherorder regularity.
- [A122706010426](https://www.ijam.latticescipub.com/portfolio-item/a122706010426/): palamadaiseetharaman@gmail.comP.N. Seetharaman, Retired Executive Engineer, Energy Conservation Cell, Tamil Nadu State Electricity Board, Anna Salai, Chennai (Tamil Nadu), India.  
- [B122405021025](https://www.ijam.latticescipub.com/portfolio-item/b122405021025/): rsivaraman1729@yahoo.co.in2Dr. R. Sivaraman, Associate Professor, Department of Mathematics, Dwaraka Doss Goverdhan Doss Vaishnav College, Arumbakkam, Chennai (Tamil Nadu), India. 
- [B122305021025](https://www.ijam.latticescipub.com/portfolio-item/b122305021025/): istepanov2001@gmail.comI.A. Stepanov, Institute of Science and Innovative Technologies, Liepaja University, Liela 14, Liepaja, LV−3401, Latvia.
- [B122205021025](https://www.ijam.latticescipub.com/portfolio-item/b122205021025/): rachu.cuty@gmail.com3Dr. Rachna Patel, Assistant Professor, Department of Computer Engineering, CGPIT, Uka Tarsadia University, Bardoli (Gujarat), India. 
- [B121905021025](https://www.ijam.latticescipub.com/portfolio-item/b121905021025/): 2Prof. Jagmohan Tanti, Department of Mathematics, Central University of Jharkhand, Ranchi (Jharkhand), India. 
- [B121805021025](https://www.ijam.latticescipub.com/portfolio-item/b121805021025/): mail2partha.ghosh@gmail.comDr. Partha Ghosh, Department of Mathematics, Abhedananda, Mahavidyalaya, Sainthia, Birbhum, West Bengal, India.
- [B121705021025](https://www.ijam.latticescipub.com/portfolio-item/b121705021025/): palamadaiseetharaman@gmail.comP.N. Seetharaman, Retired Executive Engineer, Energy Conservation Cell, Tamil Nadu State Electricity Board, Anna Salai, Chennai (Tamil Nadu), India.  
- [B121505021025](https://www.ijam.latticescipub.com/portfolio-item/b121505021025/): ssindhwani2001@gmail.comSuman Sindhwani, Associate Professor, Department of Mathematics, Hindu Girls College, Sonipat (Haryana), India. 
- [B121405021025](https://www.ijam.latticescipub.com/portfolio-item/b121405021025/): mamadou.sanghare@ucad.edu.sn3Mamadou Sanghare, Doctoral School of Mathematics-Computer – UCAD-Sénégal, University Cheikh Anta Diop of Dakar, Dakar, Senegal. 
- [B121205021025](https://www.ijam.latticescipub.com/portfolio-item/b121205021025/): doulaydem@yahoo.frDr. Abdoulaye DEMBEGA, Researcher, Department of Mathématiques, Université Norbert ZONGO, Koudougou, Burkina Faso.  
- [B121105021025](https://www.ijam.latticescipub.com/portfolio-item/b121105021025/): raghad.sahib@uokerbala.edu.iqDr. Raghad Sahib Shamsah, Department of Petroleum, Faculty of Engineering, University of Kerbala, P.O.Box 1125, Freaha, Karbala, Iraq.  
- [B120605021025](https://www.ijam.latticescipub.com/portfolio-item/b120605021025/): drjayeshk1303@gmail.comDr. Jayesh V. Karanjgaonkar, Assistant Professor, Department of Mathematics, Swami Aatmanand Govt. Eng. Med. Model College, Atari, Raipur (Chhattisgarh). 
- [B120505021025](https://www.ijam.latticescipub.com/portfolio-item/b120505021025/): anil.sharma@aot.edu.in,anil06m@gmail.comProf. Anil Kumar Sharma, Department of Engineering Science, Academy of Technology, Adisaptagram, Hooghly, India.   
- [A122506010426](https://www.ijam.latticescipub.com/portfolio-item/a122506010426/): chinmoy00123@gmail.com2Chinmoy Bhattacharya, Department of Research & Development, Austin Paints & Chemicals Pvt. Ltd., Ambika Mukherjee Road, Belghoria, Kolkata (West Bengal), India. 
- [B120005021025](https://www.ijam.latticescipub.com/portfolio-item/b120005021025/): saisns@rediffmail.comDr. Shantaram N Salunkhe, Associate Professor and Head, Department of Mathematics, Rani Laxmibai Mahavidyalaya Parola Dist. Jalgaon, (Maharashtra), India. 
- [B120105021025](https://www.ijam.latticescipub.com/portfolio-item/b120105021025/): neelamdubey03@gmail.comNeelam Dubey, Scholar, Department of Mathematics, Veer Kunwar Singh University, Ara (Bihar), India. 
- [A119405010425](https://www.ijam.latticescipub.com/portfolio-item/a119405010425/): ravi.revelly@gmail.comRavi Revelly, The Centre of Quantum Science and Technology, International Institute of Information Technology, Hyderabad, (Telangana), India.  
- [A119805010425](https://www.ijam.latticescipub.com/portfolio-item/a119805010425/): nikitadewangan18@gmail.comn2Nikita Dewangan, Scholar, Department of Mathematics, MATS University, Raipur (Chhattisgarh), India.  
- [A119605010425](https://www.ijam.latticescipub.com/portfolio-item/a119605010425/): vijayakumarmailpn@gmail.com 3P.N. Vijayakumar, B.T. Assistant in Mathematics, Gopalapuram Boys Higher Secondary School, Chennai (Tamil Nadu), India.  
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