The lowest degree 0,10,1-polynomial divisible by cyclotomic polynomial

preprint2011arXivOpen access

Abstract

Let nn be an even positive integer with at most three distinct prime factors and let $\ze_n$ be a primitive nn-th root of unity. In this study, we made an attempt to find the lowest-degree 0,10,1-polynomial $f(x) \in \Q[x]$ having at least three terms such that $f(\ze_n)$ is a minimal vanishing sum of the nn-th roots of unity.

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