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Displaying 21 – 40 of 47

On the number of integers which are sums of two squares

Yoichi Motohashi (1973)

Acta Arithmetica

On the number of representations in the Waring-Goldbach problem with a prime variable in an arithmetic progression

Maurizio Laporta (2012)

Journal de Théorie des Nombres de Bordeaux

We prove a Bombieri-Vinogradov type theorem for the number of representations of an integer $N$ in the form $N = p_{1}^{g} + p_{2}^{g} + ... + p_{s}^{g}$ with $p_{1}, p_{2}, ..., p_{s}$ prime numbers such that $p_{1} \equiv l (\mod k)$ , under suitable hypothesis on $s = s (g)$ for every integer $g \geq 2$ .

On the numbers that are representable as the sum of two cubes.

Christopher Hooley (1980)

Journal für die reine und angewandte Mathematik

On the p-adic Waring's problem

José Felipe Voloch (1999)

Acta Arithmetica

On the representation of cyclotomic polynomials as sums of squares

J. Hsia (1973)

Acta Arithmetica

On the representations of a number as a sum of squares

T. Estermann (1937)

Prace Matematyczno-Fizyczne

On the restricted Waring problem over $_{2^{n}} [t]$

Luis Gallardo (2000)

Acta Arithmetica

1. Introduction. The Waring problem for polynomial cubes over a finite field F of characteristic 2 consists in finding the minimal integer m ≥ 0 such that every sum of cubes in F[t] is a sum of m cubes. It is known that for F distinct from ₂, ₄, $_{16}$ , each polynomial in F[t] is a sum of three cubes of polynomials (see [3]). If a polynomial P ∈ F[t] is a sum of n cubes of polynomials in F[t] such that each cube A³ appearing in the decomposition has degree < deg(P)+3, we say that P is a restricted...

On the sum of two squares and two powers of k

Roger Clement Crocker (2008)

Colloquium Mathematicae

It can be shown that the positive integers representable as the sum of two squares and one power of k (k any fixed integer ≥ 2) have positive density, from which it follows that those integers representable as the sum of two squares and (at most) two powers of k also have positive density. The purpose of this paper is to show that there is an infinity of positive integers not representable as the sum of two squares and two (or fewer) powers of k, k again any fixed integer ≥ 2.

On the Waring-Goldbach problem for one square and five cubes in short intervals

Fei Xue, Min Zhang, Jinjiang Li (2021)

Czechoslovak Mathematical Journal

Let $N$ be a sufficiently large integer. We prove that almost all sufficiently large even integers $n \in [N - 6 U, N + 6 U]$ can be represented as $n = p_{1}^{2} + p_{2}^{3} + p_{3}^{3} + p_{4}^{3} + p_{5}^{3} + p_{6}^{3}, |p_{1}^{2} - \frac{N}{6}| \leq U, |p_{i}^{3} - \frac{N}{6}| \leq U, i = 2, 3, 4, 5, 6,$ where $U = N^{1 - δ + ε}$ with $δ \leq 8 / 225$ .