Question

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

• A. 2
• B. 1
• C. 0
• D. 3

Answer 1

The correct option is C 0

$(x^2-y^2)$ is even
$\therefore$ both $x$ and $y$ are even or both odd.
For both odd:
$\left[\right(2m+1)+(2n+1\left)\right]\left[\right(2m+1)-(2n+1\left)\right]=4(m+n+1)(m-n)$
For both even:
$(2m+2n)(2m-2n)=4(m+n)(m-n)$
$\Rightarrow (x+y)(x-y)$ is multiple of $4$ which is not true as per data.

Hence, the number of solutions is zero.