Four squares of primes and powers of 2

Lilu Zhao

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Four squares of primes and 165 powers of 2

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Guangshi Lü (2007)

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Corrigendum to the paper "Additive problems with prime numbers of special type" (Acta Arith. 96 (2000), 53-88)

D. I. Tolev (2002)

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Additive problems with prime numbers of special type

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Hongze Li (2006)

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Liqun Hu, Li Yang (2017)

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In this paper, we obtained that when k = 455, every pair of large even integers satisfying some necessary conditions can be represented in the form of a pair of unlike powers of primes and k powers of 2.

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Jörg Brüdern, Etienne Fouvry (1994)

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Jörg Brüdern (2014)

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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.

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Hongze Li (2001)

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On the sum of two squares and two powers of k

Roger Clement Crocker (2008)

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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. ...