Glasnik Matematicki, Vol. 56, No. 2 (2021), 241-261. \( \)

A REMARK ON FLAT TERNARY CYCLOTOMIC POLYNOMIALS

Bin Zhang

School of Mathematical Sciences, Qufu Normal University, 273165 Qufu, P. R. China
e-mail:zhangbin100902025@163.com

Abstract.   Let \(\Phi_n(x)\) be the \(n\)-th cyclotomic polynomial. In this paper, for odd primes \(p\lt q \lt r\) with \(q\equiv \pm1\pmod p\) and \(8r\equiv \pm1\pmod {pq}\), we prove that the coefficients of \(\Phi_{pqr}(x)\) do not exceed \(1\) in modulus if and only if (i) \(p=3\), \(q\geq 19\) and \(q\equiv 1\pmod 3\) or (ii) \(p=7\), \(q\geq83\) and \(q\equiv -1\pmod 7\).

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

Key words and phrases.   Flat cyclotomic polynomial, ternary cyclotomic polynomial, coefficients of cyclotomic polynomial

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https://doi.org/10.3336/gm.56.2.03

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