Question

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

• A. 1
• B. 2
• C. more than 3

Answer 1

The correct option is C more than 3

The equation can be rewritten as $p^2-q^2=388$ 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. $(-194)\times (-2)$, $194\times 2$, $(-2)\times (-194)$ and $2\times 194$.
Therefore, the number of integral solutions is 4.