On a binary Diophantine inequality involving primes of a special type

2023/12/13 by Liu, Yuhui
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2312.08565

Abstract

Let 10 and for almost all real R ∈ (N,2N], the Diophantine inequality |p₁^c+p₂^c-R|lt;(log N)^-E is solvable in prime variables p₁,p₂ such that, each of the numbers p₁+2,p₂+2 has at most [(79606)/(35740-30040c)] prime factors, counted with multiplicity. Moreover, we prove that the Diophantine inequality |p₁^c+p₂^c+p₃^c+p₄^c-N|lt;(log N)^-E is solvable in prime variables p₁,p₂,p₃,p₄ such that, each of the numbers p_i+2(i=1,2,3,4) has at most [(93801402)/(35740000-30040000c)] prime factors, counted with multiplicity.

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