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Perfect square? (Posted on 2004-07-23)

Find all integer solutions of y² = x³ - 432.

See The Solution Submitted by Nick Hobson

Rating: 3.0000 (6 votes)

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Short solution

| Comment 2 of 12 |

If x³=y²+432, then (6x)³= 6³(y²+432)= (y+36)³-(y-36)³, so (6x)³+(y-36)³=(y+36)³, which by Fermat's last theorem, is only possible some term is 0, so we need y=±36.

Posted by Oskar on 2004-07-23 13:40:31

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