2023/08/31 by Cinkir, Zubeyir, Ozturkalan, Aysegul
#Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2309.00109
We give elementary proofs of some congruence criteria to compute binomial coefficients in modulo a prime. These criteria are analogues to the symmetry property of binomial coefficients. We give extended version of Lucas Theorem by using those criteria. We give applications of these criteria by describing a method to derive identities and congruences involving sums of binomial coefficients.