Journal of Number Theory, Volume (183), No (183), Year (2017-9) , Pages (428-441)

Title : ( Some divisibility properties of binomial coefficients )

Authors: Daniel Yaqubi , Madjid Mirzavaziri ,

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In this paper, we aim to give full or partial proofs for the following three conjectures of V. J. W. Guo and C. Kratten- thaler: (1) Let a > b be positive integers, α, β be any integers and p be a prime satisfying gcd(p, a) = 1. Then there ex- ist infinitely many positive integers n for which - an+α bn+β  ≡ r (mod p) for all integers r; (2) For any odd prime p, there are no positive integers a > b such that - an bn  ≡ 0 (mod pn−1) for all n ≥ 1; (3) For any positive integer m, there exist positive integers a and b such that am > b and - amn bn  ≡ 0 (mod an−1) for all n ≥ 1.


, Binomial coefficients, p-adic valuation, Locas' theorem, Euler's totient theorem, Bernoulli numbers
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author = {Yaqubi, Daniel and Mirzavaziri, Madjid},
title = {Some divisibility properties of binomial coefficients},
journal = {Journal of Number Theory},
year = {2017},
volume = {183},
number = {183},
month = {September},
issn = {0022-314X},
pages = {428--441},
numpages = {13},
keywords = {Binomial coefficients; p-adic valuation; Locas' theorem; Euler's totient theorem; Bernoulli numbers},


%0 Journal Article
%T Some divisibility properties of binomial coefficients
%A Yaqubi, Daniel
%A Mirzavaziri, Madjid
%J Journal of Number Theory
%@ 0022-314X
%D 2017