Chen’s conjecture and its generalization

Abstract

Let l ₁, l ₂, ..., l _g be even integers and x be a sufficiently large number. In this paper, the authors prove that the number of positive odd integers k ≤ x such that (k + l ₁)², (k + l ₂)², ..., (k + l _g)² can not be expressed as 2 ⁿ + p ^α is at least c(g)x, where p is an odd prime and the constant c(g) depends only on g.

Keywords

Chen’s conjecture / Powers of 2 / Primes / Selberg’s sieve method

References

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