(1) 3(2) 2
Any others? If not, could you prove that there are no other solutions?
Actually, I have no idea. Tell me why there are no any other solutions.
p=2 gives us a compositep=3 gives us a prime numberSo, now, we examine p > 3.assume with p > 3 we get a prime number.Then p is odd. Write p = 2k+1. Then 2^p = 2^(2k+1) = 2*4^k = 2 (mod 3)since p is not equal to 3, p^2 = 1 (mod 3)hence2^p + p^2 = 2 + 1 (mod 3)= 3 (mod 3)= 0 (mod 3)There it cannot be a prime number.
With (2) use the same line of reasoning