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x and y are positive integers with the following two properties
a) x3 y3 is a perfect square, and
b) x2 y2 is a perfect cube.
Find the smallest possible values of x and y.
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My first guess , is , x=10 , y=6 .
Last edited by Stanley_Marsh (2007-04-11 02:28:13)
Numbers are the essence of the Universe
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x and y are positive integers with the following two properties
a) x3 y3 is a perfect square, and
b) x2 y2 is a perfect cube.
Find the smallest possible values of x and y.
Smallest possible values? That would be x = 1, y = 1, wouldnt it?
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All right, my answer above was trivial. I suppose you want x > y for a non-trivial solution?
In that case, by trying out the first few values on an Excel spreadsheet, I have verified that Stanleys answer is the correct one.
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