The Lowest-Degree Polynomial with Nonnegative Coefficients Divisible by the $n$-th Cyclotomic Polynomial

[摘要] We pose the question of determining the lowest-degree polynomial with nonnegative coefficients divisible by the $n$-th cyclotomic polynomial $\Phi_n(x)$. We show this polynomial is $1 + x^{n/p} + \cdots + x^{(p-1)n/p}$ where $p$ is the smallest prime divi

[学科分类] 离散数学和组合数学