A coprimality condition on consecutive values of polynomials

作者：Sanna Carlo^*; Szikszai Marton

来源：Bulletin of the London Mathematical Society, 2017, 49(5): 908-915.

DOI：10.1112/blms.12078

Let f is an element of Z[X] be a quadratic or cubic polynomial. We prove that there exists an integer G(f) >= 2 such that for every integer k >= G(f) one can find infinitely many integers n >= 0 with the property that none of f(n+1),f(n+2),...,f(n+k) is coprime to all the others. This extends previous results on linear polynomials and, in particular, on consecutive integers.

• 出版日期2017-10