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An extension of Lucas Theorem (2309.00109v1)
Published 31 Aug 2023 in math.NT and math.CO
Abstract: 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.
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