• Bulletin of the Korean Mathematical Society
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• v.54 no.1
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• pp.43-50
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• 2017

Let A(n) denote the largest absolute value of the coefficients of n-th cyclotomic polynomial ${\Phi}_n(x)$ and let p < q < r be odd primes. In this note, we give an infinite family of cyclotomic polynomials ${\Phi}_{pqr}(x)$ with A(pqr) = 3, without fixing p.

• Bulletin of the Korean Mathematical Society
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• v.52 no.6
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• pp.1911-1924
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• 2015

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).

• Bulletin of the Korean Mathematical Society
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• v.51 no.4
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• pp.949-955
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• 2014

Let ${\Phi}_n(x)={\sum}^{{\phi}(n)}_{k=0}a(n,k)x^k$ denote the n-th cyclotomic polynomial. In this note, let p < q < r be odd primes, where $q{\not{\equiv}}1$ (mod p) and $r{\equiv}-2$ (mod pq), we construct an explicit k such that a(pqr, k) = -2.