An Innovative Approach to Find Remainder
Anil Kumar Sharma
Prof. Anil Kumar Sharma, Department of Engineering Science, Academy of Technology, Adisaptagram, Hooghly, India.
Manuscript received on 03 July 2025 | First Revised Manuscript received on 27 June 2025 | Second Revised Manuscript received on 17 September 2025 | Manuscript Accepted on 15 October 2025 | Manuscript published on 30 October 202 | PP: 6-7 | Volume-5 Issue-2, October 2025 | Retrieval Number: 100.1/ijam.B120505021025 | DOI: 10.54105/ijam.B1205.05021025
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© The Authors. Published by Lattice Science Publication (LSP). This is an open-access article under the CC-BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Abstract: Let r be the remainder when x! is divided by p, (x, p) ∈ N, x < p. Then the value of r is given by the minimum value of k for which (−1) (m-1) (m-1)! k + 1 = 0(mod p), where m = p − x, k ∈ N.
Keywords: Remainder, Number Theorem, Factorial Remainder, Remainder using Wilson’s Theorem.
Scope of the Article: Number Theory