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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: a general formula | Comment 5 of 8 |
(In reply to a general formula by Ady TZIDON)

Well it's easy if one assumes Y=-Z, but I've suggested a new puzzle that investigates some other cases where this sort of question could be considered.
  Posted by broll on 2012-06-03 02:42:46

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