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.

I has been point out that have erred, and indeed I did misinterpret the problem but I'll this anyway:
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I have determined one set, but haven't been able to prove if or not it is the only one.

To that end I began with:

a²  +  b²   +   c²   =  d²

and proceeded to:

d²  -   b²  =  a²  +  c²

d²  -  b² 
----------    = 1.      
a²  +  c²           

After that I'm not sure where to go.

My set :  4 + 9 + 36 = 49, or rather  2, 3, 6 and 7.

Edited on December 11, 2008, 10:42 pm

Posted by brianjn on 2008-12-11 20:14:02