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

Explanation

`x^4 - y^4 = 37891008`

As `37891008` is an even number, it means both `x` and `y` will be even or odd.

Now, `x^4 - y^4 = (x^2+y^2)(x+y)(x-y)`

Now, `x^2+y^2, x+y and x-y` all will be divisible by `2` as both `x` and `y` are either even or odd.

So, we can write,

`x^4 - y^4 = (2a)(2b)(2c) = 8abc`, where `a,b,c` are natural numbers.

It means, `x^4-y^4` will be divisible by `8`.

But, the number `37891008` is not divisible by `8`.

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