WoS İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12573/394
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Article An Elementary Proof of Lucas's Theorem(Ramanujan Mathematical Society, 2025) Cinkir, ZubeyirLucas'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 Vander-monde identity modulo a prime number.Article An Extension of Lucas's Theorem(indian Nat Sci Acad, 2025-10-31) Cinkir, Zubeyir; Ozturkalan, AysegulWe give elementary proofs of some congruence criteria to compute binomial coefficients modulo a prime number. These criteria are analogues to the symmetry property of binomial coefficients. We give extended version of Lucas's 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.