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arXiv · 1511.03230

On the distribution of numbers related to the divisors of $x^n-1$

Sai Teja Somu
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Abstract

Let $n_1,\cdots,n_r$ be any finite sequence of integers and let $S$ be the set of all natural numbers $n$ for which there exists a divisor $d(x)=1+\sum_{i=1}^{deg(d)}c_ix^i$ of $x^n-1$ such that $c_i=n_i$ for $1\leq i \leq r$. In this paper we show that the set $S$ has a natural density. Furthermore, we find the value of the natural density of $S$.

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Sai Teja Somu. 2015-11-10. On the distribution of numbers related to the divisors of $x^n-1$. https://arxiv.org/abs/1511.03230

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