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Polinomial equation and modular arithmatic

Source: Bangladesh National Mathematical Olympiad 2015

February 25, 2019
number theoryalgebraBdmocontests2015 Contestsmodular arithmetic

Problem Statement

Let nn be a positive integer.Consider the polynomial p(x)=x2+x+1p(x)=x^2+x+1. What is the remainder of x3 x^3 when divided by x2+x+1x^2+x+1.For what positive integers values of nn is x2n+xn+1 x^{2n}+x^n+1 divisible by p(x)p(x)?
Post no:100100
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