AbstractIn this paper, we are able to sharpen Hua's classical result by showing that each sufficiently large integer N≢1(mod3) can be written asN=p+p12+p22+p32+p42,with |p−N5|⩽N5U,|pj−N5|⩽U,j=1,2,3,4, where U=N41100+ε and p, pj are primes. This result improves a previous result with U=N41100+ε replaced by U=N511+ε
AbstractLet p be a prime number, λ be an integer. We obtain new results related to the congruence x1...
AbstractLet p be a prime k|p−1, t=(p−1)/k and γ(k,p) be the minimal value of s such that every numbe...
AbstractThe main purpose of this paper is to prove a conjecture of the Euler numbers and its general...
In this paper, we prove that every sufficiently large positive integer satisfying some necessary con...
AbstractLet Pr denote an almost-prime with at most r prime factors, counted according to multiplicit...
AbstractLet N be sufficiently large odd integer. It is proved that the equation N=n1+n2+n3 has solut...
After the proof of Zhang about the existence of infinitely many bounded gaps between consecutive pri...
AbstractWe use the explicit formula of V. Shevelev for the best possible exponent α(m) in the error ...
AbstractIt is conjectured that all sufficiently large integers satisfying some necessary congruence ...
In this paper, on the assumption of the Riemann hypothesis, we give explicit upper bounds on the dif...
Let $k\geq2$ and $s$ be positive integers. Let $\theta\in(0,1)$ be a real number. In this paper, we ...
AbstractWe prove that if λ1, λ2, λ3 and λ4 are non-zero real numbers, not all of the same sign, λ1/λ...
Let $\gamma<1<c$ and $19(c-1)+171(1-\gamma)<9$. In this paper, we establish an asymptotic formula fo...
AbstractLet a(k,n) be the k-th coefficient of the n-th cyclotomic polynomials. In 1987, J. Suzuki pr...
An improved estimate is given for |θ (x) − x|, where θ (x) = p≤x log p. Four applications are give...
AbstractLet p be a prime number, λ be an integer. We obtain new results related to the congruence x1...
AbstractLet p be a prime k|p−1, t=(p−1)/k and γ(k,p) be the minimal value of s such that every numbe...
AbstractThe main purpose of this paper is to prove a conjecture of the Euler numbers and its general...
In this paper, we prove that every sufficiently large positive integer satisfying some necessary con...
AbstractLet Pr denote an almost-prime with at most r prime factors, counted according to multiplicit...
AbstractLet N be sufficiently large odd integer. It is proved that the equation N=n1+n2+n3 has solut...
After the proof of Zhang about the existence of infinitely many bounded gaps between consecutive pri...
AbstractWe use the explicit formula of V. Shevelev for the best possible exponent α(m) in the error ...
AbstractIt is conjectured that all sufficiently large integers satisfying some necessary congruence ...
In this paper, on the assumption of the Riemann hypothesis, we give explicit upper bounds on the dif...
Let $k\geq2$ and $s$ be positive integers. Let $\theta\in(0,1)$ be a real number. In this paper, we ...
AbstractWe prove that if λ1, λ2, λ3 and λ4 are non-zero real numbers, not all of the same sign, λ1/λ...
Let $\gamma<1<c$ and $19(c-1)+171(1-\gamma)<9$. In this paper, we establish an asymptotic formula fo...
AbstractLet a(k,n) be the k-th coefficient of the n-th cyclotomic polynomials. In 1987, J. Suzuki pr...
An improved estimate is given for |θ (x) − x|, where θ (x) = p≤x log p. Four applications are give...
AbstractLet p be a prime number, λ be an integer. We obtain new results related to the congruence x1...
AbstractLet p be a prime k|p−1, t=(p−1)/k and γ(k,p) be the minimal value of s such that every numbe...
AbstractThe main purpose of this paper is to prove a conjecture of the Euler numbers and its general...
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