Hello. I've got three questions.

1.Can a Mersenne number be a multiple of another Mersenne number? Prove. (I mean is that possible that 2^a - 1 | 2^b - 1 where a, b are prime numbers)

2.Can a Mersenne number be equal to X^n ? (X and n are integer). Prove. (This Mersenne number is 2^d - 1 where d is a prime number)

3.Is it possible that (2^t - 1)^a * (2^u - 1)^b is equal to 2^tu - 1? (t, u, 2^t -1, 2^u -1 are prime numbers).