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

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• 作者：Sai Teja Somu ^{somuteja@gmail.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Distribution of coefficients of divisors of xn&minus ; 1xn&minus ; 1 ; Coefficients of divisors ; Coefficients of divisors of xn&minus ; 1xn&minus ; 1 ; Coefficients of cyclotomic polynomials ; Cyclotomic polynomials ; On the distribution of numbers related ; Natural density of coefficients
• 刊名：Journal of Number Theory
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：170
• 期：Complete
• 页码：3-9
• 全文大小：234 K

文摘

Let n₁,⋯,n_r$n_1,\cdots ,n_r$ be any finite sequence of integers and let S be the set of all natural numbers n   for which there exists a divisor $d(x)=1+{\sum }_{i=1}^{deg(d)}{c}_i{x}^i$ of xⁿ&minus;1$x^n\&<font\; color="red">minus</font>;1$ such that c_i=n_i$c_i=n_i$ for 1≤i≤r$1\le i\le r$. In this paper we show that the set S has a natural density. Furthermore, we find the value of the natural density of S.