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Glasnik matematički, Vol. 58 No. 1, 2023.

Original scientific paper

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

On the coefficients of a class of ternary cyclotomic polynomials

Bin Zhang ; School of Mathematical Sciences, Qufu Normal University, 273165 Qufu, P. R. China

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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 \(p\lt q \lt r\)
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 \(q\equiv 1\pmod 5\).

Keywords

Cyclotomic polynomial, Coefficients of cyclotomic polynomial, Flat ternary cyclotomic polynomial, Non-flat ternary cyclotomic polynomial.

Hrčak ID:

304387

URI

https://hrcak.srce.hr/304387

Publication date:

20.6.2023.

Visits: 209 *

Publication date: 30 June 2023

Volume: Vol 58

Issue: Svezak 1

Pages: 17-34

DOI: 10.3336/gm.58.1.02

Article Information (continued)

Categories:

Subject: Izvorni znanstveni članak

Keywords:

Keyword: Cyclotomic polynomial, Coefficients of cyclotomic polynomial, Flat ternary cyclotomic polynomial, Non-flat ternary cyclotomic polynomial.

On the coefficients of a class of ternary cyclotomic polynomials

Bin Zhang[1]

Email: zhangb2015@qfnu.edu.cn

 

[1] School of Mathematical Sciences, Qufu Normal University, 273165 Qufu, P. R. China

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 \(p\lt q \lt r\) 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 \(q\equiv 1\pmod 5\).

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