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Four special natural numbers (Posted on 2008-12-11) Difficulty: 2 of 5
Find all sets of four natural numbers such that the square of each of them, when added to the sum of the other three, again yields a perfect square.

See The Solution Submitted by pcbouhid    
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Some Thoughts re: Is there a pattern to this? Comment 8 of 8 |
(In reply to Is there a pattern to this? by brianjn)

For the sets that contain a 1, the pattern apparently is that any (q^2-1)/3 that is an integer (two out of every three are) will work as the other three.

The problem is indeed those erratic ones that don't contain a 1.

  Posted by Charlie on 2008-12-12 11:18:18
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