BD-BDMO 2015 Problem 3

Let $n$ be a positive integer.Consider the polynomial $p(x)=x^2+x+1$ . What is the remainder of $x^3$ when divided by $x^2+x+1$ .For what positive integers values of $n$ is $x^{2n}+x^n+1$ divisible by $p(x)$ ?

Post no: $100$