Goldbach-Linnik Problem on Unlike Powers of Primes and Powers of Two

Abstract

It is proved that every sufficiently large odd number can be expressed as a sum of one prime, four prime cubes and 9 powers of 2. This improves the previous result for k = 15. Also, when k = 27, every sufficiently large even integer can be represented in a sum of eight cubes of primes and k powers of 2. This is an improvement of previous result for k = 28.

Keywords

Circle method / Linnik problem / powers of two / 11P32 / 11P05 / 11P55

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Peking University