Glasnik Matematicki, Vol. 58, No. 1 (2023), 17-34. \( \)

ON THE COEFFICIENTS OF A CLASS OF TERNARY CYCLOTOMIC POLYNOMIALS

Bin Zhang

School of Mathematical Sciences, Qufu Normal University, 273165 Qufu, P. R. China
e-mail:zhangb2015@qfnu.edu.cn

Abstract.   A cyclotomic polynomial \(\Phi_n(x)\) is said to be flat if its nonzero coefficients involve only \(\pm1\). In this paper, for odd primes \( p \le q \le r \) with \(q\equiv 1\pmod p\) and \(9r\equiv \pm1\pmod {pq}\), we prove that \(\Phi_{pqr}(x)\) is flat if and only if \(p=5\), \(q\geq 41\), and \(q\equiv 1\pmod 5\).

2020 Mathematics Subject Classification.   11B83, 11C08, 11N56.

Key words and phrases.   Cyclotomic polynomial, Coefficients of cyclotomic polynomial, Flat ternary cyclotomic polynomial, Non-flat ternary cyclotomic polynomial.

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https://doi.org/10.3336/gm.58.1.02

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