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

Options

A. 0
B. 1
C. 2
D. 4

Answer

A

Explanation

Since 3789108 is an even integer. Therefore `x^(4)-y^(4)` is also an evenn integer. So either both x and y are even integers or both of them are odd integers.
Now `x^(4)-y^(4)=(x-y)(x+y)(x^(2)y^(2))`
`impliesx-y,x+y,x^(2)+y^(2)` must be even integers.
Therefore `(x-y)(x+y)(x^(2)+y^(2))` must be divisibel by 8. But 3789108 is not divisible by 8. Hence, the given equation has no solution.
`:.` Number of solutions `=0`