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Topic: From Fermat little theorem to Fermat Last Theorem
Replies: 62   Last Post: Mar 14, 2013 9:59 PM

 Messages: [ Previous | Next ]
 Michael Klemm Posts: 133 Registered: 11/13/12
Re: From Fermat little theorem to Fermat Last Theorem
Posted: Jan 7, 2013 4:46 PM

John Jens wrote:

> a^p?a(mod p)
> a^p = a + px it's obvious that x is positive integer

Yes, and in the same way

b^p = b + py
and
c^p = c + pz.

Up to now you may assume
a^p + b^p = c^p
where p is a prime >= 2
and 0 < a <= b < c,
a, b, c integers.

You correctly conclude in (1) that
a + b - c > 0.

Further by Fermat's little theorem
p (z-x-y) = a + b - c.

Therefore
z-x-y >= 1 and thus
a > a + b - c >= p.

So it seems to me that you also disprove the case p = 2.

Regards
Michael

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