AbstractIn 1979 R. Apéry introduced the numbers an = Σ0n(kn)2(kn + k) and un = Σ0n(kn)2(kn + k)2 in his irrationality proof for ζ(2) and ζ(3). We prove some congruences for these numbers which generalize congruences previously published in this journal
AbstractLet Q(−k) be an imaginary quadratic field with discriminant −k and class number h, with k≠3,...
In this article we introduce Proth numbers and prove two theorems on such numbers being prime [3]. W...
AbstractWe study properties of the polynomials φk(X) which appear in the formal development Πk − 0n ...
AbstractApéry introduced a recurrence relation for a proof of the irrationality of ζ(3). Let an (n ≥...
AbstractIn 1979 R. Apéry introduced the numbers an = Σ0n(kn)2(kn+k)2 in his irrationality proof for ...
AbstractCongruences for the Apéry numbers are proved which generalize the results and conjectures of...
AbstractA congruence modulo 8 is proved relating the class numbers of the quadratic fields Q(√p) and...
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 ...
AbstractWe give a p-adic proof of a certain new relation between the Bernoulli numbers Bk, similar t...
AbstractLet p ≥ 5 be a prime and a, b, c relatively prime integers such that ap + bp + cp = 0. A the...
AbstractThe three sequences mentioned in the title are Ramanujan's τ-function, the coefficients cn o...
AbstractIf b(m;n) denotes the number of partitions of n into powers of m, then b(m; mr+1n) ≡ b(m; mr...
AbstractLet p be an odd prime and γ(k,pn) be the smallest positive integer s such that every integer...
AbstractIn 1979 R. Apéry introduced the numbers an = Σ0n(kn)2(kn + k) and un = Σ0n(kn)2(kn + k)2 in ...
AbstractLet Q(−k) be an imaginary quadratic field with discriminant −k and class number h, with k≠3,...
In this article we introduce Proth numbers and prove two theorems on such numbers being prime [3]. W...
AbstractWe study properties of the polynomials φk(X) which appear in the formal development Πk − 0n ...
AbstractApéry introduced a recurrence relation for a proof of the irrationality of ζ(3). Let an (n ≥...
AbstractIn 1979 R. Apéry introduced the numbers an = Σ0n(kn)2(kn+k)2 in his irrationality proof for ...
AbstractCongruences for the Apéry numbers are proved which generalize the results and conjectures of...
AbstractA congruence modulo 8 is proved relating the class numbers of the quadratic fields Q(√p) and...
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 ...
AbstractWe give a p-adic proof of a certain new relation between the Bernoulli numbers Bk, similar t...
AbstractLet p ≥ 5 be a prime and a, b, c relatively prime integers such that ap + bp + cp = 0. A the...
AbstractThe three sequences mentioned in the title are Ramanujan's τ-function, the coefficients cn o...
AbstractIf b(m;n) denotes the number of partitions of n into powers of m, then b(m; mr+1n) ≡ b(m; mr...
AbstractLet p be an odd prime and γ(k,pn) be the smallest positive integer s such that every integer...
AbstractIn 1979 R. Apéry introduced the numbers an = Σ0n(kn)2(kn + k) and un = Σ0n(kn)2(kn + k)2 in ...
AbstractLet Q(−k) be an imaginary quadratic field with discriminant −k and class number h, with k≠3,...
In this article we introduce Proth numbers and prove two theorems on such numbers being prime [3]. W...
AbstractWe study properties of the polynomials φk(X) which appear in the formal development Πk − 0n ...
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