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

Options:

A . 0

B . 1

C . 2

D . 3

E . more than 3

Answer: Option E : E option (e)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 x 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)

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