x^16 - y^8 + 345y^2 divisible by 15?

[uptowngirl92]

If x and y are positive integers, is x^16 - y^8 + 345y^2 divisible by 15?

x is a multiple of 25, and y is a multiple of 20
y=x^2

[navalpike]

I would go with B.

2.
Since S2 is easier, take that first.
If y = x^2, then the original equation becomes
X^16-x^16+345y^2/15
Or
345y^2/15
Since 15 goes into 345, the equation is divisible by 15. Sufficient

1. If one item divisible by 15 is added to or subtracted from another item divisible by 15, then the result is divisible by 15. We already know that 345y^2 is divisible by 15, but we cannot be sure about x and y.

If x is divisible by 25, then x^16 is a multiple of 25. However in order for it to be a multiple of 15 (primes 5 & 3), it needs at least one 3. We cannot be certain that is has that 3.

Same goes for Y.

Insuff.