Proof that $n$ is prime when $1+x+x^2+...+x^{n-1}$ = ${1-x^n}\over{1-x}$ is prime. Given $x$ and $n$ are positive integers and $1+x+x^2+...+x^{n-1}$ is a prime number.
Then prove that $n$ is a prime number.
Can the formula $1+x+x^2+...+x^{n-1} = \dfrac{1-x^n}{1-x}$ be somehow used?

An equivalent statement is that if $n = km$ then $\frac {1-x^n} {1-x}$ is also composite. See how you can use the formula $1+x+x^2+...+x^{n-1} = \frac {1-x^n} {1-x}$ to factorize $\frac {1-x^{km}} {1-x}$.
