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The smallest sum II (Posted on 2012-06-10) Difficulty: 3 of 5

See The smallest sum.

1. Show that there are no positive integers {X,Y,Z} (with Z less than Y less than X) such that X+Y, X-Y, X+Z, X-Z, Y+Z, Y-Z are all squares; or provide a counter-example.

2. Assuming that no counter-example exists, what is the minimum such set {X,Y,Z} for which each of X+Y, X-Y, X+Z, X-Z, and either of Y+Z or Y-Z, are all squares?

See The Solution Submitted by broll    
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  Subject Author Date
re: computer solution for part 1 (spoiler)broll2012-06-12 00:31:51
Solutioncomputer solution for part 1 (spoiler)Steve Herman2012-06-11 10:11:40
Solutioncomputer solution for part 2 (spoiler)Charlie2012-06-10 20:29:42
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