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Archiv der Mathematik

, Volume 78, Issue 5, pp 386–396 | Cite as

A note on a conjecture of Borwein and Choi

  • R. Thangadurai

Abstract.

A polynomial P(X) with coefficients {±1} of odd degree N - 1 is cyclotomic if and only if¶¶\( P(X) = \pm \Phi_{p1} (\pm X)\Phi_{p2}(\pm X^{p1}) \cdots \Phi_{p_r}(\pm X^{p1 p2 \cdots p_r-1}) \)¶where N = p 1 p 2···p r and the p i are primes, not necessarily distinct, and where \( \Phi_{p}(X) := (X^{p} - 1) / (X - 1) \) is the p-th cyclotomic polynomial. This is a conjecture of Borwein and Choi [1]. We prove this conjecture for a class of polynomials of degree \( N - 1 = 2^{r} p^{\ell} - 1 \) for any odd prime p and for integers \( r, \ell \geqq 1 \).

Keywords

Cyclotomic Polynomial 
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Copyright information

© Birkhäuser Verlag, Basel 2002

Authors and Affiliations

  • R. Thangadurai
    • 1
  1. 1.The Institute of Mathematical Sciences, C.I.T. Campus, Taramani, Chennai 600 113, India,¶ e-mail: thanga@imsc.ernet.inIN

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