Find all pairs of prime numbers p and q that satisfy the equation 3p^q-2q^p-1=19.

(In reply to solution by xdog)

Given that q is odd, we have 2q^p-1 + 19=1 mod4 but 3p^q=3 mod4. Therefore, any solution requires q=2 and the equation becomes 3p^2-2^p=19. 

Posted by jiyaca on 2023-07-18 00:26:46