Polynomials Consisting of Quadratic Factors with Roots Modulo Any Positive Integer

Abstract

We give an infinite family of polynomials that have roots modulo every positive integer but fail to have rational roots. Each polynomial in this family is made up of monic quadratic factors that do not have linear term.

Cited by in corpus (2)

• Polynomials with factors of the form $(x^q-a)$ with roots modulo every integer
• Minimally Intersective Polynomials with Arbitrarily Many Quadratic Factors