Each of X and Y is a positive integer which is not a perfect square that satisfy:

√X - √Y = √17

Is each of X and Y always divisible by 17?

Give reasons for your answer.

If x, y and z are integers, and sqrt(x) - sqrt(y) = sqrt(z),

then x and y are divisible by z whenever z is not divisible by a perfect square. So, for instance, z = 10 works but z = 12 does not. This is a simple generalization of the proof I already posted.

Also, if x, y and z are integers, and sqrt(x) + sqrt(y) = sqrt(z),

then x and y are divisible by z whenever z is not divisible by a perfect square.