Question 1
(CZS) (a) Find all natural numbers $n$ such that the number $2^n-1$ is divisible by $7$.
(b) Prove that for all natural numbers $n$ the number $2^n+1$ is not divisible by $7$.
(b) Prove that for all natural numbers $n$ the number $2^n+1$ is not divisible by $7$.