2006

Abstract

The condition of the problem is equivalent to each of the following statements: the polynomial $(x^3+x^2+x+1)^n+x^n$ is divisible by $Q(x)=x^4+x^3+x^2+x+1,$ or $(-x^4)^n+x^n$ is divisible by Q(x),  or $(-1)^nx^{3n}+1$ is divisible by Q(x).