Cyclotomic ordering conjecture

Abstract

This note describes a conjecture involving cyclotomic polynomials and some initial thoughts towards a solution. Given positive integers $m,n$, the conjecture is that either ${\Phi }_m(q)⩽{\Phi }_n(q)$ or ${\Phi }_m(q)⩾{\Phi }_n(q)$ holds for all integers $q⩾2$. Pomerance and Rubinstein-Salzedo proved the conjecture in a preprint called `Cyclotomic coincidences' [arXiv:1903.01962].

2 pages; Pomerance and Rubinstein-Salzedo wanted to be able to cite my conjecture for their paper "Cyclotomic coincidences" [arXiv:1903.01962]