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Question


Find the number of integral solutions of the equation p2=388+q2.


Options:
A .   0
B .   1
C .   2
D .   more than 3
E .   can’t be determined
Answer: Option D
:
D

The equation can be rewritten as p2q2=388 or (p+q)(p-q) = 388.
The number of ways in which 388 can be expressed as a product of two numbers such that p and q are integral is 4, i.e. (194)×(2), 194×2(2)×(194) and 2×194.
Therefore, the number of integral solutions is 4.



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