AbstractApéry introduced a recurrence relation for a proof of the irrationality of ζ(3). Let an (n ≥ 0) satisfy the relation n3an − (34n3 − 51n2 + 27n − 5)an − 1 + (n − 1)3an − 2 = 0. Which values of a0 and a1 cause each an to be an integer? This question is answered and some congruence properties of the an are given
AbstractThe aim of this paper is to show that for any n∈N, n>3, there exist a, b∈N* such that n=a+b,...
AbstractApéry introduced a recurrence relation for a proof of the irrationality of ζ(3). Let an (n ≥...
AbstractLet p ≥ 5 be a prime and a, b, c relatively prime integers such that ap + bp + cp = 0. A the...
AbstractIn 1979 R. Apéry introduced the numbers an = Σ0n(kn)2(kn + k) and un = Σ0n(kn)2(kn + k)2 in ...
AbstractCongruences for the Apéry numbers are proved which generalize the results and conjectures of...
AbstractIn 1979 R. Apéry introduced the numbers an = Σ0n(kn)2(kn+k)2 in his irrationality proof for ...
AbstractWe prove that Apéry numbers satisfy an analog mod p, p2 and p3 of the congruence of Lucas fo...
AbstractThe Apéry numbers, introduced in Apéry's celebrated proof of the irrationality of ζ(3), are ...
AbstractLet β be an irrational number. For t ≥ 1, put ψβ(t)= minp,qint 0<q⩽t | qβ − p |, μ∗(β)= supt...
AbstractA congruence modulo 8 is proved relating the class numbers of the quadratic fields Q(√p) and...
AbstractLet p be an odd prime and γ(k,pn) be the smallest positive integer s such that every integer...
AbstractLet α > 1. Denoting by [x] the integer part of x, we give complete answers to the following ...
AbstractIf b(m;n) denotes the number of partitions of n into powers of m, then b(m; mr+1n) ≡ b(m; mr...
AbstractWe give a p-adic proof of a certain new relation between the Bernoulli numbers Bk, similar t...
AbstractLetRbe a UFD andpa prime ofR. Letl1a1,…,lrarbe prime top. In this paper a formula is derived...
AbstractThe aim of this paper is to show that for any n∈N, n>3, there exist a, b∈N* such that n=a+b,...
AbstractApéry introduced a recurrence relation for a proof of the irrationality of ζ(3). Let an (n ≥...
AbstractLet p ≥ 5 be a prime and a, b, c relatively prime integers such that ap + bp + cp = 0. A the...
AbstractIn 1979 R. Apéry introduced the numbers an = Σ0n(kn)2(kn + k) and un = Σ0n(kn)2(kn + k)2 in ...
AbstractCongruences for the Apéry numbers are proved which generalize the results and conjectures of...
AbstractIn 1979 R. Apéry introduced the numbers an = Σ0n(kn)2(kn+k)2 in his irrationality proof for ...
AbstractWe prove that Apéry numbers satisfy an analog mod p, p2 and p3 of the congruence of Lucas fo...
AbstractThe Apéry numbers, introduced in Apéry's celebrated proof of the irrationality of ζ(3), are ...
AbstractLet β be an irrational number. For t ≥ 1, put ψβ(t)= minp,qint 0<q⩽t | qβ − p |, μ∗(β)= supt...
AbstractA congruence modulo 8 is proved relating the class numbers of the quadratic fields Q(√p) and...
AbstractLet p be an odd prime and γ(k,pn) be the smallest positive integer s such that every integer...
AbstractLet α > 1. Denoting by [x] the integer part of x, we give complete answers to the following ...
AbstractIf b(m;n) denotes the number of partitions of n into powers of m, then b(m; mr+1n) ≡ b(m; mr...
AbstractWe give a p-adic proof of a certain new relation between the Bernoulli numbers Bk, similar t...
AbstractLetRbe a UFD andpa prime ofR. Letl1a1,…,lrarbe prime top. In this paper a formula is derived...
AbstractThe aim of this paper is to show that for any n∈N, n>3, there exist a, b∈N* such that n=a+b,...
AbstractApéry introduced a recurrence relation for a proof of the irrationality of ζ(3). Let an (n ≥...
AbstractLet p ≥ 5 be a prime and a, b, c relatively prime integers such that ap + bp + cp = 0. A the...
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