Math Is Fun Forum

math123

Member

Registered: 2007-04-11

Posts: 1

Algebra

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.

Stanley_Marsh

Member

Registered: 2006-12-13

Posts: 345

Re: Algebra

My first guess , is , x=10 , y=6 .

Last edited by Stanley_Marsh (2007-04-11 02:28:13)

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Numbers are the essence of the Universe

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Algebra

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, wouldn’t it?

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Algebra

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 Stanley’s answer is the correct one.