On the distribution of numbers related to the divisors of xⁿ-1

2015/11/10 by Sai Teja Somu, Somu, Sai Teja
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1511.03230

6 pages, submitted to Journal of Number Theory

arxiv created 2015/11/10 · arxiv updated 2015/11/11

Abstract

Let n₁,⋯,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+∑_i=1^deg(d)c_ixⁱ of xⁿ-1 such that c_i=n_i for 1≤ i ≤ 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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