Find the number of integral solutions of the equation p2=388+q2
The equation can be rewritten as p2−q2 =388. the number of ways in which 388 can be expressed as difference of squares in one way as 388 is a prime multiple of 4 ( 4 × 97). However, since the question is about integral solutions, the total number of ways in which it can be expressed will be 4 (2 cases for p, positive and negative and 2 cases for q)