IS my proof of the fermat's last theorem correct? check it at http://spaces.msn.com/spideyunlimited so?

Answer 1

Your reasoning: suppose (a,b,c,n) is an integer solution to
[1] ... a^n + b^n = c^n
Then (taking the derivative w.r.t. n)
[2] ... a^n ln a + b^n ln b = c^n ln c
must be true.

** THIS IS NOT CORRECT **
With the same argument, I could prove that the equation x = -x has no solutions; for if it did, then dx/dx = -dx/dx, that is, 1 = -1, which cannot be the case.
The only thing you show is that the functions a^n + b^n and c^n cannot be indentical, i.e. true for every (real) value of n.
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You also claim that
[3] ... a^n ln a + b^n ln b = 0
has no solutions for positive natural numbers a, b and n>2.

*** THIS IS NOT RELEVANT AND NOT CORRECT ***
First of all, if this argument would be relevant then it would also hold for n = 2. You would have proven that there are no Pythagorean triples, i.e. integers (a, b, c) such that a^n + b^n = c^n. However, such triples do exist, as the example 3^2 + 4^2 = 5^2 shows.
Secondly, it is not even true. If a = b = 1 then ln a = ln b = 0, making [3] true.
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Finally, you suggest that if a function has no minimum or maximum value, there cannot be solutions involving that function. That is not true. The equation x^3 + x = 5 has a solution, even though d(x^3 + x)/dx = 3x^2 + 1 has no zeroes.

Answer 2

There are too many problems here
1) a b c are integers so at the point they are not differentiable
2) d(a^n)/dn is not possible as n is not a continuous function
If we take your analogy then a^2+b^2 = c^2 also cannot be true 3rd ly this is maximum or minimum when the derivative is zero and all that is ab c are increasing indefinitely

Answer 3

Without looking - either:

1) You know Andrew Willey's solution OR
2) Unlikely. The reason being that it was unsolved in over 300 years - and the proof was over 100 pages and took months to verify.

From looking at your effort: I don't think differential calculus is transitive - but the concept is good.

Answer 4

Your first mistake is when you take a derivative of the equation. Since it is not a functional equation, but a discrete equation, that is not allowed.

Also, FLT *has* been proved! It was done by Andrew Wiles.