#### Vol. 4, No. 4, 2011

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The family of ternary cyclotomic polynomials with one free prime

### Yves Gallot, Pieter Moree and Robert Wilms

Vol. 4 (2011), No. 4, 317–341
##### Abstract

A cyclotomic polynomial ${\Phi }_{n}\left(x\right)$ is said to be ternary if $n=pqr$, with $p$, $q$ and $r$ distinct odd primes. Ternary cyclotomic polynomials are the simplest ones for which the behavior of the coefficients is not completely understood. Here we establish some results and formulate some conjectures regarding the coefficients appearing in the polynomial family ${\Phi }_{pqr}\left(x\right)$ with $p, $p$ and $q$ fixed and $r$ a free prime.

##### Keywords
ternary cyclotomic polynomial, coefficient
Primary: 11C08
Secondary: 11B83