Hi
how can i show that if 2^(n-1) is prime then n is prime?
thank you
I guess you meant $\displaystyle 2^n-1$, so that the question is less trivial...
Let $\displaystyle d\geq 0$ be a diviser of $\displaystyle n$. Write $\displaystyle n=d\times q$. Apply the formula $\displaystyle a^q-1=(a-1)(1+a+\cdots+a^{q-1})$ to $\displaystyle a=2^d$ to conclude that $\displaystyle 2^d-1$ divides $\displaystyle 2^n-1$. Since $\displaystyle 2^n-1$ is prime, this means $\displaystyle 2^d-1=0$ or $\displaystyle 2^d-1=2^n-1$, hence $\displaystyle d=0$ ou $\displaystyle d=n$. This proves that $\displaystyle n$ is prime.