After several attempts with geometry and gymnastics with number theory, what I believe I found a general proof and simple one as Fermat would wish. But anyway, I am not skilled in Matematics, nor in any subject except chemistry, I just get sometimes the creative ideas.... So I got one last night...I would really like to ask you guyz, where is the mistake?As probably there is one.

 

Proof: Let us suppose that a,b,c are coprimes, so if we construct the from a,b,c the smallest triangle for solution of the Fermats Last Theorem. so lets suppose that the sollution exist, a^n + b^n = c^n so if we sqare the equation it will hold true that (a^n + b^n)^2 = (c^n)^2 so -----> a^2n + b^2n + 2a^nb^n = c^2n ----------> 2a^nb^n = c^2n - b^2n - a^2n, from the number theory we know that it follows that c^2n - b^2n is devidable by a^n, so c^2n - b^2n = a^n*k where k is the element of natural numbers. so lets multiply the original Fermats equation by factor k, so ------> a^n*k + b^n*k = c^n*k, lets now substitute the term a^n*k by c^2n - b^2n so:-------> c^2n - b^2n + b^n*k = c^n*k -------->b^n*(k - b^n) = c^n*(k - c^n), since b and c are coprimes b^n = (k - c^n)*m and c^n = (k - b^n)*m where m again is the element of Natural numbers. so--------> c^n + b^n*m = b^n + c^n*m, we see that m is 1, so -----> k = c^n + b^n lets now put that into 2a^nb^n = c^2n - b^2n - a^2n -----------> lets divide now the whole eqation by a^n ----------------> 2b^n = c^n + b^n - a^2 -------------> b^n = c^n - a^2 and since a^n + b^n = c^n ---------> b^n = a^n + b^n - a^2 ------------> a^n = a^2 -------------> n = 2 if the solution of the fermats last theorem exists.

Robert Kulovec Mueller, Slovenija

 

correction: k is the element of odd numbers, not natural

 

 

At the risk of sounding ignorant, I must ask, why should [math]c^{2n}-b^{2n}[/math] be divisible by [math]a^{n}[/math]?

DIdn't you just post this nonsense elsewhere?

 

Other than the minor problem that your proof is essentially unreadable, the real problem is here:

 

2a^nb^n = c^2n - b^2n - a^2n -----------> lets divide now the whole eqation by a^n ----------------> 2b^n = c^n + b^n - a^2

 

Bzzzt, wrong. Dividing a²ⁿ by aⁿ yields aⁿ, not a².