Journal of the Ramanujan Mathematical Society
Volume 40, Issue 4, December 2025 pp. 385–387.
An elementary proof of Lucas's Theorem
Authors:
Zubeyir Cinkir
Author institution:Department of Industrial Engineering, Abdullah Gul University, 38100, Kayseri, Turkey.
Summary:
Lucas's Theorem is about finding the result of a binomial
coefficient modulo a prime p efficiently. The result is
expressed as a product of binomial coefficients involving
the base p expansions of the parameters of the original binomial
coefficient. We give an elementary proof of Lucas's Theorem
by deriving an analogous Vandermonde identity modulo a prime
number.
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