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Math Forum / Mathematics / General Topics / September 2004Fermat's last theorem (New)
Fermat's Last Theorem Ben T. Ito 9-29-04 I will solve Fermat's last theorem. 1. Introduction Fermat implied that there was a simple proof that for X^n + Y^n = Z^n only n=2 forms integer solutions that describe lengths X, Y and Z. 2. Proof Using the lengths X=3 and Y=4, when n is at infinity and approaches two, the length Z approaches five. At n=2, Z=5 which forms an integer solution that forms a right triangle. An infinite number of proportional right triangles solutions can be formed using, X=3m, Y=4m, and Z=5m, equ 1 where m=1,2,3,4............ . An infinite number of integer solutions are formed when the right triangle are formed using proportional right triangles, of equation l, when n=2 ; therefore, only right triangles, when n=2, form integer solutions. 3. Conclusion I have formed an infinite number of solutions, using proportional right triangles, that only form integer solutions when n=2 which completes the proof of Fermat's last theorem. Sonya Stewart. -------------------------------------------------------------------------------- > Fermat's Last Theorem > Ben T. Ito [quoted text clipped - 37 lines] > ** SPEED ** RETENTION ** COMPLETION ** ANONYMITY ** > ---------------------------------------------------------- Instead of blindly restating your 'proof' over and over again, (JSH tactics), it may be nice to answer questions also. I'll restate mine: Can you give an argument, based on your own proof, why there is not a certain Z and n>2 such that, for example, 17^n + 53^n = Z^n ??? Your proof sounds something like: because I can form an infinite number of solutions for n=2, there just cannot be other solutions. Strange... Jeroen > > I will solve Fermat's last theorem. > > I have formed an infinite number of solutions, using proportional > > right triangles, that only form integer solutions when n=2 which > > completes the proof of Fermat's last theorem. > Your proof sounds something like: because I can form an infinite number > of solutions for n=2, there just cannot be other solutions. Strange... Oh, I think it's quite nice. For example, if you have 4 objects in a set, and you can show that 4 objects in that set are elephants, then it follows that every member of S is an elephant. Indeed, for any finite number N, if a set S has N members, and if N members of S have a certain property, then all members of S have that property. Now using the fact that infinity is a finite number -- oh, I know this may be counterintuitive, but that's just because crafty Cantorians *named* things to make it seem like infinity is infinite -- so, again, using the fact that infinity is a finite number, we can prove a variety of things. For example, let S be the set of solutions of X^n + Y^n = Z^n. An infinite number of them occur for n=1, so all solutions occur for n=1. In particular, none occur for n>2. Or for n=2, for that matter. And this holds whether you're working in the ring of integers, or some neo-Harrisian object ring. On the other hand, because there are an infinite number of solutions to X^n + Y^n = Z^n, all 4-tuples (X,Y,Z,n) are solutions. Etc. The thing I like about this method is that it gives Cantor cranks something to talk about with Fermat cranks. And cranks are usually such solitary creatures. > I will solve Fermat's last theorem. Cool. Go on to prove Goldbach's conjecture as well. Since there are infinite odd primes, you can add 3 to each of them, thus producing an infinity of even numbers which are a sum of two primes. QED. Dimitris On 30 Sep 2004, George wrote: >benito20044@yahoo-dot-com.no-spam.invalid (ben ito) wrote in message news:<415bad40$1_2@127.0.0.1>... >> Fermat's Last Theorem [quoted text clipped - 35 lines] > I don't see in any case that from this we can conclude that only when >n=2 we have only integer solutions. I think that the point is that none of the solutions for X, Y and Z which "work" for n = 2 will work for n > 2. But even if this is the case, what about all other possible combinations of X, Y and Z? Why would we only want to a Pythagorean triple? >> 3. Conclusion >> [quoted text clipped - 14 lines] >> ** SPEED ** RETENTION ** COMPLETION ** ANONYMITY ** >> ---------------------------------------------------------- Geert |
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