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A litmus test, what about n=2
Posted:
Aug 26, 1996 2:21 PM


I remember reading that one of the faults of false methods of proving FLT is that they disprove it for n=2 as well. What I've found doesn't do that but it does establish interesting limitations on x,y and z for n=2.
When I first started with this I amused myself by noting that a solution to x^2 + y^2 = z^2 could be found for any odd x by making y=(x^2  1)/2
like 3,4,5; or 5,12,13; or 7,24,25;
I also found the case 8,15,17 from a math book. So, I've wondered if there were any possibilities where zx or zy had prime factors other than one or 2.
I'm saying now that they can't for the same reasons that I give which prove FLT.
No natural number counterexamples exist for the above.
That litmus test passed.
James Harris



