Question

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

• A. $1$
• B. $2$
• C. $0$
• D. $4$

Answer 1

The correct option is C $0$

$x^4-y^4=3789108$

Since R.H.S is a even integer, so L.H.S is also an even integer.

So, either both $x$ or $y$ are even integer or both of them are odd integers.

Now,

$x^4-y^4=(x-y)(x+y)(x^2+y^2)$

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

$\therefore (x-y)(x+y)(x^2+y^2)$ must be divisible by $8$. But R.H.S is not divisible by $8$.

Hence the given equation has no solution.