1. If xy^(2) and xy are perfect squares, where x and y are positive integers, what is the smallest value of x + y?

Question

1. If x
`y^(2)` and xy are perfect squares, where x and y are positive integers, what is the smallest value of x + y?

Answer 1

8

Explanation:

xy^2 = k*k y^2 x = k * k so x has to be a perfect square.

xy is a perfect square which means that since x is a perfect square (see above) then y will have to be as well

There is nothing that prohibits x = 4 and y = 4 as being the answer where x = y.

I think the smallest possible value for x + y is 8.

This excludes any possibility of 1 or 0 in some combination, although I would look into 1.