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On the representation of integer as sum of a square-free number and a prime of special type

Published 11 Jan 2025 in math.NT | (2501.06622v2)

Abstract: We prove that there are infinitely many integers, which can represent as sum of a square-free integer and a prime $p$ with $||\alpha p+\beta||<p{-1/10}$, where $\alpha$ is irrational.

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