# ON A CLASS OF TERNARY CYCLOTOMIC POLYNOMIALS

• ZHANG, BIN (School of Mathematical Sciences Qufu Normal University) ;
• ZHOU, YU (School of Mathematical Sciences Nanjing Normal University)
• Published : 2015.11.30
• 93 14

#### Abstract

A cyclotomic polynomial ${\Phi}_n(x)$ is said to be ternary if n = pqr for three distinct odd primes p < q < r. Let A(n) be the largest absolute value of the coefficients of ${\Phi}_n(x)$. If A(n) = 1 we say that ${\Phi}_n(x)$ is flat. In this paper, we classify all flat ternary cyclotomic polynomials ${\Phi}_{pqr}(x)$ in the case $q{\equiv}{\pm}1$ (mod p) and $4r{\equiv}{\pm}1$ (mod pq).

#### Keywords

ternary cyclotomic polynomial;flat cyclotomic polynomial;coefficient of cyclotomic polynomial

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#### Cited by

1. Remarks on the flatness of ternary cyclotomic polynomials vol.13, pp.02, 2017, https://doi.org/10.1142/S1793042117501354