Bin Zhang: A family of non-flat ternary cyclotomic polynomials, 89-95

Abstract:

Let $\Phi_n(x)$ be the $n$-th cyclotomic polynomial, $p<q<r$ be odd primes, and $z$ be an integer such that $zr\equiv\pm1\pmod {pq}$. There have been extensive studies about the flatness of ternary cyclotomic polynomials $\Phi_{pqr}(x)$ for special cases of $z$. We present some classes of non-flat ternary cyclotomic polynomials for the general cases of $z$.

Key Words: Coefficients of cyclotomic polynomial, ternary cyclotomic polynomial, non-flat cyclotomic polynomial.

2010 Mathematics Subject Classification: Primary 11B83; Secondary 11C08.

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