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arXiv · 1604.03885

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

Zhivko Petrov·Doychin Tolev
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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.

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Zhivko Petrov, Doychin Tolev. 2016-04-17. On an equation involving fractional powers with one prime and one almost prime variables. https://arxiv.org/abs/1604.03885

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