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Topic: A litmus test, what about n=2
Replies: 2   Last Post: Sep 5, 1996 4:20 AM

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James Harris

Posts: 16
Registered: 12/12/04
A litmus test, what about n=2
Posted: Aug 26, 1996 2:21 PM
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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 z-x or z-y 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 counter-examples exist for the above.

That litmus test passed.

James Harris

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