I need a hel for find out the answers for the followinf number theory, prime number questions, please give me a help to find out the answers

1.) If p is prime prove that there exist no positive integers a and b s.t. a^2 = pb^2

2.) If [(2^n) -1] is a prime, the n is also a prime

3.) If n>= 5 is a prime number, show that n^2 + 2 is not a prime.

4.) If b(not= 2) is a prime number show that b^2 + (b + 2)^2 + (b + 4)^2 +1 is divisible by 12.

please see the attached file for better understanding of the question