A short note on some arithmetical properties of the integer part of $\alpha p$

Authors: YILDIRIM AKBAL

Abstract: Let $\alpha>0$ be an irrational number. We study some of the arithmetical properties of $\{ \fl{\alpha p}\}_{p=2}^{\infty}$, where $p$ denotes a prime number and $\fl{x}$ denotes the largest integer not exceeding $x$.

Keywords: Arithmetic progressions, Beatty sequences, exponential sums, shifted primes

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