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.
sqrt(x) = sqrt(17) + sqrt(y)
x = 17 + y + 2sqrt(17y)
the LHS is integer. so the RHS is also, so y must be a multiple of 17
sqrt(y) = -sqrt(17) + sqrt(x)
y = 17 + x - 2sqrt(17x)
the LHS is integer. so the RHS is also, so x must be a multiple of 17
Note that this is true for any x and y, even if x or y is a perfect square