It looks like you edited this comment, but I'm serious. I'm trying to understand...

It looks like you edited this comment, but I'm serious. I'm trying to understand your proof, but I'm having trouble seeing what the steps are for higher powers than 3 or 4. I already know the proofs for then cases n=3 and n=4, but I can't see how what you say works in the case, say, n=5, or n=13.

Seriously, can you walk us through the steps of why x^5+y^5=z^5 has no (non-trivial) solutions?

And to be fair, there are cases where, say, undergrads have proven significant results that had been outstanding for a long time. Proving that prime recognition is in P is one such case. but in that case they published a complete, clear paper. In this case I can't really see what you're saying you've done, or why it's true, which is why a walk-through of the case n=5 would be so helpful.

Thanks.

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For anyone interested, this is what the comment used to say ...

The series of odd numbers must be consecutive and they simply are not when you add two different series together for all powers greater than two. It's okay. You'll get it.

  1) a whole number, n, taken
     to a power greater than two
  2) can be represented as a
     consecutive series of odd
     numbers
  3) where there will always be
     a gap in the series between
     consecutive base numbers,
     for all p and p+1
  4) therefore there will be
     a gap for all p and p+n,
     n>=1 combinations