Question

Find the number of integral solutions of the equation $p^2=388+q^2$

• A. 1
• B. 2
• C. 3
• D. more than 3

Answer 1

The correct option is D more than 3

the equation can be rewritten as $p^2-q^2=388$. the number of ways in which 388 can be expressed as difference of squares in one way as 388 is a prime multiple of $4(4\times 97)$. 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