Lucas Theorem

Problem introduction

Given three numbers n, r, and p, compute the above value of $\binom{n}{r}$% p.

Lucas theorem approach

In number theory, the Lucas’ Theorem expresses the remainder of the division of the binomial coefficient $\binom{n}{r}$ by a prime number p in terms of base p expansions of integers n and r.

The Lucas Theorem suggests that the value of $\binom{n}{r}$ ...