AbstractLet N be sufficiently large odd integer. It is proved that the equation N=n1+n2+n3 has solutions, where ni has a fixed number of prime factors, and an asymptotic formula holds for the number of representations
AbstractBy using the Newton interpolation formula, we generalize the recent identities on the Catala...
Let \u3c8K be the Chebyshev function of a number field K. Let \u3c8K(1)(x) := 2b0x\u3c8K(t) dt and \...
AbstractLetM(n) be the largest integer that can be expressed as a sum of the reciprocal of distinct ...
AbstractThe main purpose of this paper is to prove a conjecture of the Euler numbers and its general...
AbstractWe use the explicit formula of V. Shevelev for the best possible exponent α(m) in the error ...
AbstractA new expansion is given for partial sums of Eulerʼs pentagonal number series. As a corollar...
AbstractWe consider some parametrized classes of multiple sums first studied by Euler. Identities be...
AbstractIn this paper, we are able to sharpen Hua's classical result by showing that each sufficient...
Contains a correction with respect to the printed versionWe provide sharp estimates for the number o...
AbstractThis note is a continuation of a paper by the same authors that appeared in 2002 in the same...
AbstractIn this paper we obtain an improved asymptotic formula on the frequency of k-free numbers wi...
AbstractIt is conjectured that all sufficiently large integers satisfying some necessary congruence ...
In this paper, we show under the abc conjecture that the Diophantine equation f(x)=u!+v! has only fi...
AbstractAs a generalization of Calkin's identity and its alternating form, we compute a kind of bino...
An improved estimate is given for |θ (x) − x|, where θ (x) = p≤x log p. Four applications are give...
AbstractBy using the Newton interpolation formula, we generalize the recent identities on the Catala...
Let \u3c8K be the Chebyshev function of a number field K. Let \u3c8K(1)(x) := 2b0x\u3c8K(t) dt and \...
AbstractLetM(n) be the largest integer that can be expressed as a sum of the reciprocal of distinct ...
AbstractThe main purpose of this paper is to prove a conjecture of the Euler numbers and its general...
AbstractWe use the explicit formula of V. Shevelev for the best possible exponent α(m) in the error ...
AbstractA new expansion is given for partial sums of Eulerʼs pentagonal number series. As a corollar...
AbstractWe consider some parametrized classes of multiple sums first studied by Euler. Identities be...
AbstractIn this paper, we are able to sharpen Hua's classical result by showing that each sufficient...
Contains a correction with respect to the printed versionWe provide sharp estimates for the number o...
AbstractThis note is a continuation of a paper by the same authors that appeared in 2002 in the same...
AbstractIn this paper we obtain an improved asymptotic formula on the frequency of k-free numbers wi...
AbstractIt is conjectured that all sufficiently large integers satisfying some necessary congruence ...
In this paper, we show under the abc conjecture that the Diophantine equation f(x)=u!+v! has only fi...
AbstractAs a generalization of Calkin's identity and its alternating form, we compute a kind of bino...
An improved estimate is given for |θ (x) − x|, where θ (x) = p≤x log p. Four applications are give...
AbstractBy using the Newton interpolation formula, we generalize the recent identities on the Catala...
Let \u3c8K be the Chebyshev function of a number field K. Let \u3c8K(1)(x) := 2b0x\u3c8K(t) dt and \...
AbstractLetM(n) be the largest integer that can be expressed as a sum of the reciprocal of distinct ...
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