Question

The number of positive integral solutions of $x^2-y^2=352706$ is

• A. 0
• B. 1
• C. 2
• D. none of these

Answer 1

The correct option is A 0

Now $352706$ is an even function
$\therefore x^2-y^2=2m\Rightarrow$ either both $x,y$ are even or both $x,y$ are odd.
In any case both $x+y$ and $x-y$ are even integers.
$2(x+y)2(x-y)=4(x^2-y^2)$ $\Rightarrow 4(x^2-y^2)\Rightarrow \frac{4}{352706}$
But it is not true as $06$ is not divisible by $4$.
So number of integer solution is $0$.