Polynomials (x3 − n)(x2 + 3) Solvable Modulo Any Integer
Andrea M. Hyde, Paul D. Lee, Blair Kenneth Spearman · American Mathematical Monthly · 2014
We give an infinite family of polynomials that are solvable modulo m for every integer m > 1, yet have no roots in the rational numbers. Such polynomials are called intersective. Our classification uses only techniques available in an undergraduate course in number theory.