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

On the greatest common divisor of integer parts of polynomials