Displaying similar documents to “Distribution of integers that are sums of three squares of primes”

Four squares of primes and powers of 2

Lilu Zhao (2014)

Acta Arithmetica

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By developing the method of Wooley on the quadratic Waring-Goldbach problem, we prove that all sufficiently large even integers can be expressed as a sum of four squares of primes and 46 powers of 2.

On the sum of two squares and two powers of k

Roger Clement Crocker (2008)

Colloquium Mathematicae

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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 pairs of Goldbach-Linnik equations with unequal powers of primes

Enxun Huang (2023)

Czechoslovak Mathematical Journal

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It is proved that every pair of sufficiently large odd integers can be represented by a pair of equations, each containing two squares of primes, two cubes of primes, two fourth powers of primes and 105 powers of 2.

On Sums of Four Coprime Squares

A. Schinzel (2013)

Bulletin of the Polish Academy of Sciences. Mathematics

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It is proved that all sufficiently large integers satisfying the necessary congruence conditions mod 24 are sums of four squares prime in pairs.

Sums of Squares Coprime in Pairs

Jörg Brüdern (2014)

Bulletin of the Polish Academy of Sciences. Mathematics

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Asymptotic formulae are provided for the number of representations of a natural number as the sum of four and of three squares that are pairwise coprime.