A coprimality condition on consecutive values of polynomials

Autor:	Márton Szikszai, Carlo Sanna
Rok vydání:	2017
Předmět:	Combinatorics Quadratic equation Integer Coprime integers General Mathematics 010102 general mathematics Integer sequence 010103 numerical & computational mathematics 0101 mathematics 01 natural sciences Cubic function Mathematics
Zdroj:	Bulletin of the London Mathematical Society. 49:908-915
ISSN:	0024-6093
DOI:	10.1112/blms.12078
Popis:	Let $f\in\mathbb{Z}[X]$ be quadratic or cubic polynomial. We prove that there exists an integer $G_f\geq 2$ such that for every integer $k\geq G_f$ one can find infinitely many integers $n\geq 0$ with the property that none of $f(n+1),f(n+2),\dots,f(n+k)$ is coprime to all the others. This extends previous results on linear polynomials and, in particular, on consecutive integers.
Databáze:	OpenAIRE
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