MathDB

A2

Part of 2020 Romanian Master of Mathematics Shortlist

Problems(1)

My best problem

Source: RMM 2020 Shortlist

10/15/2021
Let n>1n>1 be a positive integer and S\mathcal S be the set of nthn^{\text{th}} roots of unity. Suppose PP is an nn-variable polynomial with complex coefficients such that for all a1,…,an∈Sa_1,\ldots,a_n\in\mathcal S, P(a1,…,an)=0P(a_1,\ldots,a_n)=0 if and only if a1,…,ana_1,\ldots,a_n are all different. What is the smallest possible degree of PP?
Adam Ardeishar and Michael Ren
algebra