On the greatest common divisor of integer parts of polynomials

William Banks; Igor E. Shparlinski

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arXiv · 2205.00253

On the greatest common divisor of integer parts of polynomials

William Banks·Igor E. Shparlinski

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Abstract

Motivated by a question of V. Bergelson and F. K. Richter (2017), we obtain asymptotic formulas for the number of relatively prime tuples composed of positive integers $n\le N$ and integer parts of polynomials evaluated at $n$. The error terms in our formulas are of various strengths depending on the Diophantine properties of the leading coefficients of these polynomials.

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William Banks, Igor E. Shparlinski. 2022-04-30. On the greatest common divisor of integer parts of polynomials. https://arxiv.org/abs/2205.00253

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