An Innovative Approach to Find Remainder - Prof. Anil Kumar Sharma, (Indian Journal of Advanced Mathematics (IJAM), 2025)
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.