The number of positive integral solutions of the equation $x^2-y^2=3906$ is

Question

Professor PC Thomas Classes · Answer

$(\mathrm{x}-\mathrm{y})(\mathrm{x}+\mathrm{y})=3906$ ∴ one of $\mathrm{x}-\mathrm{y}$ and $\mathrm{x}+\mathrm{y}$ is even. If one of them is even then the other also is even. This implies that $(\mathrm{x}-\mathrm{y})(\mathrm{x}+\mathrm{y})$ is divisible by 4 . But 3906 is not divisible by 4 . Therefore there is no solution.