Intersective Polynomials Arising from Sums of Powers

Abstract

Given a natural number $n\ge 2$, an integer $k$ and for a judiciously chosen $l=l(n)$ we give necessary and sufficient conditions for the polynomial $f_{n,k}=\left({\sum }_{i=1}^l{x}_i^n\right)-k$ to have roots modulo every positive integer.

arXiv comment13 pages, 5 tables, Published Online in Comm. Alg. (DOI given)