AbstractLet Pr denote an almost-prime with at most r prime factors, counted according to multiplicity. In this paper it is proved that any sufficiently large integer N satisfying the congruence condition N≡13(mod240) can be represented as the sum of twelve fourth powers of primes and the fourth power of one P5. This result constitutes an improvement upon that of Ren and Tsang
AbstractIn this paper, it is proved that every sufficiently large odd integer is a sum of a prime, f...
After the proof of Zhang about the existence of infinitely many bounded gaps between consecutive pri...
AbstractWe prove that if λ1, λ2, λ3 and λ4 are non-zero real numbers, not all of the same sign, λ1/λ...
In this paper, we prove that every sufficiently large positive integer satisfying some necessary con...
AbstractIn this paper, we are able to sharpen Hua's classical result by showing that each sufficient...
AbstractIt is conjectured that all sufficiently large integers satisfying some necessary congruence ...
AbstractWe study the representations of large integers n as sums p12+⋯+ps2, where p1,…,ps are primes...
AbstractWe prove a Bombieri–Vinogradov type result for linear exponential sums over primes. Then we ...
AbstractLet p be an odd prime and γ(k,pn) be the smallest positive integer s such that every integer...
AbstractIt is conjectured that all sufficiently large integers satisfying some necessary congruence ...
Let $k\geq2$ and $s$ be positive integers. Let $\theta\in(0,1)$ be a real number. In this paper, we ...
AbstractIt is conjectured that Lagrange's theorem of four squares is true for prime variables, i.e. ...
We prove that the density of integers ≡2 (mod 24), which can be represented as the sum of two square...
AbstractIn this paper we continue our study, begun in G. Harman and A.V. Kumchev (2006) [10], of the...
AbstractWe prove that for almost all n, the numerator of the Bernoulli number B2n is divisible by a ...
AbstractIn this paper, it is proved that every sufficiently large odd integer is a sum of a prime, f...
After the proof of Zhang about the existence of infinitely many bounded gaps between consecutive pri...
AbstractWe prove that if λ1, λ2, λ3 and λ4 are non-zero real numbers, not all of the same sign, λ1/λ...
In this paper, we prove that every sufficiently large positive integer satisfying some necessary con...
AbstractIn this paper, we are able to sharpen Hua's classical result by showing that each sufficient...
AbstractIt is conjectured that all sufficiently large integers satisfying some necessary congruence ...
AbstractWe study the representations of large integers n as sums p12+⋯+ps2, where p1,…,ps are primes...
AbstractWe prove a Bombieri–Vinogradov type result for linear exponential sums over primes. Then we ...
AbstractLet p be an odd prime and γ(k,pn) be the smallest positive integer s such that every integer...
AbstractIt is conjectured that all sufficiently large integers satisfying some necessary congruence ...
Let $k\geq2$ and $s$ be positive integers. Let $\theta\in(0,1)$ be a real number. In this paper, we ...
AbstractIt is conjectured that Lagrange's theorem of four squares is true for prime variables, i.e. ...
We prove that the density of integers ≡2 (mod 24), which can be represented as the sum of two square...
AbstractIn this paper we continue our study, begun in G. Harman and A.V. Kumchev (2006) [10], of the...
AbstractWe prove that for almost all n, the numerator of the Bernoulli number B2n is divisible by a ...
AbstractIn this paper, it is proved that every sufficiently large odd integer is a sum of a prime, f...
After the proof of Zhang about the existence of infinitely many bounded gaps between consecutive pri...
AbstractWe prove that if λ1, λ2, λ3 and λ4 are non-zero real numbers, not all of the same sign, λ1/λ...
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