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## Fermat’s Last Theorem

Here is a terrific video talking about two of the greatest mathematical problem solvers, Fermat and Andrew Wiles.    It is great insight into the life of Wiles, the genius who solved Fermat’s Last Theorem.

### 3 Responses

1. on July 13, 2013 at 11:34 am | Reply Peter L. Griffiths

Fermat’s Last Theorem can be proved by finding the integer nth root of
(p +q)^n -(p -q)^n, without p equalling q.
This involves binomial expansions and distinguishing
rational from irrational numbers, particularly converting the irrational
number of 2^(1/n) into the rational number of 2.

2. on February 25, 2016 at 11:07 am | Reply Peter L. Griffiths

Take the nth root of both sides
[(1 +1/r)^n – (1 -1/r)^n]^1/n = 2^1/n [(n*1)1/r + (n*3) 1/r^3 …]^1/n.
Let r =1, so that p=q. This deliberately converts the 3 term assumption of FLT into 2 terms. Hence when r =1 and p=q, there are just 2 terms,
[(n*1) + (n*3)…..]^1/n = 2^(1- 1/n).
It also follows that provided n is greater than 2 the Pythagorean triples power, and provided the 3 term assumption is restored, [(n*1) 1/r + (n*3)1/r^3 …]^1/n will be less than 2 when multiplied by by 2^1/n. there can only be equality with 2 terms not the the 3 terms assumed in Fermat’s Last Theorem. The Wiles Proof of Fermat’s Last Theorem lacks any explanation of the absence of the power n=2 being the Pythagorean triples situation from the conclusions of FLT. This could mean that the whole proof is wrong particularly since it is only thought to be understood by a small clique of mathematicians.

3. on March 3, 2017 at 8:06 am | Reply Peter L. Griffiths

Containing less than 300 words, my full proof of Fermat’s Last theorem is in the February 2017 issue of M500,