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

T. L. Todorova

We prove that there are infinitely many integers, which can represent as sum of a square-free integer and a prime $p$ with $||\hat{I}\pm p+{\hat{I}}^2||<p^{-1/10}$, where $\hat{I}\pm$ is irrational.