On Arithmetic Progressions of Powers in Cyclotomic Polynomials

Abstract

We determine necessary conditions for when powers corresponding to positive/negative coefficients of ${\Phi }_n$ are in arithmetic progression. When $n=pq$ for any primes $q>p>2$, our conditions are also sufficient. Finally, we generalize the result when $n=pq$ to the so-called inclusion-exclusion polynomials first introduced by Bachman.

arXiv comment6 pages. Generalized the result when $n=pq$ to the so-called inclusion-exclusion polynomials first introduced by Bachman