A property of cyclotomic polynomials

Abstract

Given two cyclotomic polynomials ${\Phi }_n(x)$ and ${\Phi }_m(x)$, $n\ne m$, we determine the minimal natural number k such that we can write $$k=a(x){\Phi }_n(x)+b(x){\Phi }_m(x),$$ with a(x) and b(x) integer polynomials.

4 pages, Problem 10914 in Amer. Math. Monthly 109 (Jan 2002)