Goldbach-Linnik type problems for mixed powers of primes and powers of 2

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Abstract

Let p₁,p₂, ... ,p₇ be primes. In this paper, we first show that when k₁ = 23, every sufficiently large odd integer can be represented as the sum of one prime square, five prime cubes, one prime biquadrate and at most k₁ powers of 2. We further prove that for k₂ = 45, every pair of sufficiently large odd integers satisfying certain necessary conditions can be represented as a pair of equations involving one prime square, five prime cubes, one prime biquadrate and at most k₂ powers of 2.

Keywords

circle method / exponential sums / Goldbach-Linnik type problem / powers of 2 / primes

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