On an equation involving fractional powers with one prime and one almost prime variables

Zhivko Petrov; Doychin Tolev

On an equation involving fractional powers with one prime and one almost prime variables

Number Theory 2016-04-19 v2

Authors: Zhivko Petrov , Doychin Tolev

Abstract

In this paper we consider the equation $[p^{c}] + [m^{c}] = N$ , where $N$ is a sufficiently large integer, and prove that if $1 < c < \frac{29}{28}$ , then it has a solution in a prime $p$ and an almost prime $m$ with at most $\left[ \frac{52}{29 - 28 c}\right] + 1$ prime factors.

Keywords

fractional powers prime variable almost prime variable diophantine equation number theory integer solutions

Cite

@article{arxiv.1604.03885,
  title  = {On an equation involving fractional powers with one prime and one almost prime variables},
  author = {Zhivko Petrov and Doychin Tolev},
  journal= {arXiv preprint arXiv:1604.03885},
  year   = {2016}
}

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