An exercise regarding polynomials I guess it is a simple exercise though I'm not very good at polynomials. It asks:
Find $m,n,p,q$ natural numbers such that the polynomial $X^m+X^n+X^p+X^q$ is divisible by $x^3+x^2+x+1$.
Thank you in advance.

Hint: $$1+x+x^2+x^3=(1+x)+x^2(1+x)=(1+x)(1+x^2)$$
