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arXiv · 2010.02668

An Identity involving the Cyclotomic Polynomials

Pablo L. De Nápoli
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Abstract

We present an elementary identity for the cyclotomic polynomials $\Phi_n(X)$ which reflects a kind of multiplicative property of $\Phi_n(X)$ as a function of $n$, and we explore its connections with the properties of other arithmetical functions. Important Note: In the first version of this article uploaded to the arXiv, it is said that this result seemed to be new. However, after that, I have learned that this identity (in Theorem 1.1) has previously appeared in Cheng, C. C. A., McKay, J. H., & Wang, S. S. S. (1995). Resultants of cyclotomic polynomials. Proceedings of the American Mathematical Society, 123(4), 1053-1059. (with a different proof).

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Pablo L. De Nápoli. 2020-10-06. An Identity involving the Cyclotomic Polynomials. https://arxiv.org/abs/2010.02668

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