Steinberger: low-degree nonnegative cyclotomic multiples

---

Library card, especially Theorems 1 and 2 and the zero-sum-array certificate construction.

John P. Steinberger, "The lowest-degree polynomial with nonnegative coefficients divisible by the $n$-th cyclotomic polynomial," The Electronic Journal of Combinatorics 19 (2012), no. 4, P1.

The paper asks for the least degree of a nonzero polynomial with nonnegative coefficients divisible by $\Phi_n$. It translates the problem to multidimensional cyclotomic arrays: fibers represent prime cycles, and dual zero-sum arrays provide linear-programming certificates. The main theorem settles broad families, including even $n$, prime powers, and a range controlled by a reciprocal-prime inequality.