On the greatest common divisor of integer parts of polynomials
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 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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