Question

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

• A. 1
• B. 2
• C. 4

Answer 1

Since RHS is even. So LHS is also even integer so either both x and y should be even or both should be odd integer.
Now $x^4-y^4=(x-y)(x+y)(x^2+y^2)$
$(x-y),(x+y),(x^2+y^2)$ must be an even integer
Therefore $(x-y),(x+y),(x^2+y^2)$ must be divisible by 8
But RHS is not divisible by 8
So given equation has no solution