AbstractThe Erdős–Moser conjecture states that the Diophantine equation Sk(m)=mk, where Sk(m)=1k+2k+⋯+(m−1)k, has no solution for positive integers k and m with k⩾2. We show that stronger conjectures about consecutive values of the function Sk, that seem to be more naturally, imply the Erdős–Moser conjecture
Paul Erdos conjectured that for every n ∈ N, n ≥ 2, there exist a, b, c natural numbers, not necessa...
AbstractWe prove that the product of k consecutive terms of a primitive arithmetic progression is ne...
AbstractWe show that for A ranging over n×n circulants with three ones in each row, where n is prime...
AbstractThe Erdős–Moser conjecture states that the Diophantine equation Sk(m)=mk, where Sk(m)=1k+2k+...
If k is a sufficiently large positive integer, we show that the Diophantine equation n(n+d)⋯(n+(k−1...
AbstractThe following two facts are shown: 1.(i) There is a computable constant γ > 0 such that, giv...
A particular case of a conjecture of Erdös and Graham, which concerns the number of integer points o...
AbstractErdős estimated the maximal number of integers selected from {1,2,…,N}, so that none of them...
AbstractWe prove a special case of a conjecture of Erdős and Rosenfeld regarding factor– dif...
AbstractIt is proven that the Diophantine equation x2 + 11 = 3n has as its only solution (x, n) = (4...
AbstractThe Euler–Lehmer constants γ(a,q) are defined as the limitslimx→∞(∑n⩽xn≡a(modq)1n−logxq). We...
We study integers n > 1 satisfying the relation σ(n) = γ(n)², where σ(n) and γ(n) are the sum of div...
AbstractLet a, b, c, d be given nonnegative integers with a,d⩾1. Using Chebyshevʼs inequalities for ...
We study integers n > 1 satisfying the relation σ(n) = γ(n)², where σ(n) and γ(n) are the sum of div...
Paul Erdos conjectured that for every n ∈ N, n ≥ 2, there exist a, b, c natural numbers, not necessa...
Paul Erdos conjectured that for every n ∈ N, n ≥ 2, there exist a, b, c natural numbers, not necessa...
AbstractWe prove that the product of k consecutive terms of a primitive arithmetic progression is ne...
AbstractWe show that for A ranging over n×n circulants with three ones in each row, where n is prime...
AbstractThe Erdős–Moser conjecture states that the Diophantine equation Sk(m)=mk, where Sk(m)=1k+2k+...
If k is a sufficiently large positive integer, we show that the Diophantine equation n(n+d)⋯(n+(k−1...
AbstractThe following two facts are shown: 1.(i) There is a computable constant γ > 0 such that, giv...
A particular case of a conjecture of Erdös and Graham, which concerns the number of integer points o...
AbstractErdős estimated the maximal number of integers selected from {1,2,…,N}, so that none of them...
AbstractWe prove a special case of a conjecture of Erdős and Rosenfeld regarding factor– dif...
AbstractIt is proven that the Diophantine equation x2 + 11 = 3n has as its only solution (x, n) = (4...
AbstractThe Euler–Lehmer constants γ(a,q) are defined as the limitslimx→∞(∑n⩽xn≡a(modq)1n−logxq). We...
We study integers n > 1 satisfying the relation σ(n) = γ(n)², where σ(n) and γ(n) are the sum of div...
AbstractLet a, b, c, d be given nonnegative integers with a,d⩾1. Using Chebyshevʼs inequalities for ...
We study integers n > 1 satisfying the relation σ(n) = γ(n)², where σ(n) and γ(n) are the sum of div...
Paul Erdos conjectured that for every n ∈ N, n ≥ 2, there exist a, b, c natural numbers, not necessa...
Paul Erdos conjectured that for every n ∈ N, n ≥ 2, there exist a, b, c natural numbers, not necessa...
AbstractWe prove that the product of k consecutive terms of a primitive arithmetic progression is ne...
AbstractWe show that for A ranging over n×n circulants with three ones in each row, where n is prime...
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