Displaying similar documents to “Lagrange's Four Squares Theorem with almost prime variables.”

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. ...