An Innovative Approach to Find Remainder

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.

Authors

Publication Details

Journal
Indian Journal of Advanced Mathematics
Published
2025-10-29
DOI
https://doi.org/10.54105/ijam.b1205.05021025
Primary Topic
Advanced Mathematical Theories
Type
article
Field-Weighted Citation Impact
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article

An Innovative Approach to Find Remainder

Prof. Anil Kumar Sharma
Indian Journal of Advanced Mathematics
Advanced Mathematical Theories
article

An Innovative Approach to Find Remainder

Prof. Anil Kumar Sharma
article en

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.

Indian Journal of Advanced MathematicsVol. 5(2)
Openalex Percentile: Top 62%
Advanced Mathematical Theories
DOIOpen Access PDFOpenAlex
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An Innovative Approach to Find Remainder — Prof. Anil Kumar Sharma · Indian Journal of Advanced Mathematics (2025) | TGRS Research Map | TGRS