Question

The number of positive integral solution of $x^4-y^4=3789108$

• A. $0$
• B. $1$
• C. $2$
• D. $4$

Answer 1

The correct option is A $0$

Given equation is $x^4-y^4=3789108$

Since $x^4-y^4$ is an even integer, so either both $x$ and $y$ are

even integers or both of them are odd integers.

Either way $x-y$, $x+y$, $x^2+y^2$ must be even integers.

Therefore $x^4-y^4=(x-y)(x+y)(x^2+y^2)$ must be divisible by $8$

However, $3789108$ is not divisible by $8$.

$\therefore$ the given equation has no solution.

Hence, option A is correct.