Prove that:

if a and b are positive integers with (a, b) = 1, and if ab is a perfect square,

then a and b are perfect squares.

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- Feb 14th 2009, 12:36 AMmancillaj3n
Prove that:

if a and b are positive integers with (a, b) = 1, and if ab is a perfect square,

then a and b are perfect squares. - Feb 14th 2009, 06:35 AMred_dog
Let

Let . Then

Then . But or . Suppose that

In the same way, suppose .

Then

So,

Then