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Square+27 (Posted on 2019-01-22)

Find all positive integers x > y > z such that x²+27y, y²+27z, z²+27x and x²+y²+z²+27 are all perfect squares.

No Solution Yet Submitted by Danish Ahmed Khan

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Example but no proof

Comment 2 of 2 |

With the aid of a computer program, I can confirm that 108, 75, 72 is a solution, and the only solution for x <= 1000. But I don't have a proof that there are no others.

Posted by Paul on 2019-01-23 20:15:42

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