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The smallest sum (Posted on 2012-06-02) Difficulty: 3 of 5
Find three distinct integers, X, Y and Z, such that X + Y, X + Z, Y + Z, X - Y, X - Z, and Y - Z are all squares of integers.
Apparently, there are many solutions.

Find the set [X, Y, Z] with the smallest X + Y + Z.

No Solution Yet Submitted by Ady TZIDON    
Rating: 4.6667 (3 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re(2): a general formula | Comment 6 of 8 |
(In reply to re: a general formula by broll)

Taking the first few X values, 17,68,82,97,153, and placing them into Sloane, does not yield any formula. It's not an arithmetic progression; so I'm wondering what the easy general formula is, even counting the fact that Z=-Y.
  Posted by Charlie on 2012-06-03 10:35:34

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