Fermat's Last theorem short proof
in [Math]
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From: Dik T. Winter on 27 Feb 2007 20:04 In article <689545.1172620604015.JavaMail.jakarta(a)nitrogen.mathforum.org> bassam king karzeddin <bassam(a)ahu.edu.jo> writes: Please, do retain attributions of the articles you are responding to. Randy Poe: > > > All right, you didn't answer but somebody else e did. I have > > > now seen a validation of this identity including g the > > > statement that N(x,y,z) = 1 for p = 3. > > See my proof of it in my previous article. For p = 1, N(x,y,z) = 0 and > > for p = 3, N(x, y, z) = 1. That is also easily proven: (x + y + z)^p > > - x^p - y^p - x^p is a homogenous polynomial of degree 3, and so it is > > 3.(x + y)(x + z)(y + z). For p= 5 it is: > > x^2 + x.y + x.z + y^2 + y.z + z^2. > > Where is your previous article please In the newsgroup <news:JE3IDr.2A5(a)cwi.nl>. -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/
From: Hisanobu Shinya on 27 Feb 2007 11:46 > > > > Hello TO ALL > > > > > > > > The only remaining case -PROOF > > > > > > > > Now, you may easily derive the following > > identity > > > for > > > > a counter example when (p) is a prime factor > OF > > > > (x*y*z) > > > > > > > > Let x^p + y^p = z^p, where (x,y,z) are three > > > positive > > > > coprime integers, then the following identity > > must > > > > hold > > > > > > > > (x*y*z)^p = > > (x+y)*(z-x)*(z-y)*N(x,y,z) > > > > > > > where > > > > > > > > > > > Gcd((x+y)*(z-x)*(z-y), N(x,y,z))= p, > > > > > > > Very Simple to prove, (no need to waste time > on > > > > that) > > > > > > > > Now, (p^k*p) divides the left hand side of the > > > above > > > > identity, where as p^(k*p-1) only divides the > > > right > > > > hand side of the above Identity, where k is > > > positive > > > > integer number,and as I had shown you today > from > > > > other post. > > > > > > > > Therefore, the identity can't hold true with > > > integer > > > > numbers defined above AND THERE IS NO COUNTER > > > > EXAMPLE > > > > > > > > Hence THE PROOF IS INDEED COMPLETED > > > > > > SORRY, a flaw was found by me few hours after > > posting > > > proof of this case and it is no more valid, but > I > > > have another one > > > > I will be happy to read another argument. > > > > > > > > > You may add any suitable references, and then > > > write > > > > it in any suitable languge, beside let the > > > JOURNALS > > > > KNOW ABOUT IT > > > > > > > > > > > > > > > > > > > > > > MY BEST REGARDS > > > > > > > > Bassam Karzeddin > > > > > > > > AL Hussein bin Talal University > > > > > > > > JORDAN > > I have already corrected that argument Actually, I had not even asked what the mistake was. > > B.Karzeddin
From: Hisanobu Shinya on 27 Feb 2007 12:15 > > > > > > > Fermat's Last theorem short proof > > > > > > > > > > > > > > We have the following general equation > > > (using > > > > > the > > > > > > > general binomial theorem) > > > > > > > > > > > > > > (x+y+z)^p =p* (x+y)*(x+z)*(y+z)*N(x,y,z) > + > > > > > > > x^p+y^p+z^p > > > > > > > > > > > > > > Where > > > > > > > N (x, y, z) is integer function in terms > > of > > > > (x, > > > > > y, > > > > > > z) > > > > > > > > > > > > > > P is odd prime number > > > > > > > (x, y, z) are three (none zero) co prime > > > > > integers? > > > > > > > > > > > > > > Assuming a counter example (x, y, z) > > exists > > > > such > > > > > > that > > > > > > > (x^p+y^p+z^p=0) > > > > > > > > > > > > > > > > > > > > > (x+y+z)^p =p* (x+y)*(x+z)*(y+z)*N (x, y, > z) > > > > > > > > > > > > > > > > CASE-1 > > > > > > > If (p=3) implies N (x, y, z) = 1, so we > > have > > > > > > > > > > > > > > > Why? > > > > > > > > > > All right. I got this, and I think this is > > > clever. > > > > > > > > > > > > > > > > > > > > > > > > > (x+y+z)^3 =3* (x+y)*(x+z)*(y+z) > > > > > > > > > > > > > > Assuming (3) does not divide (x*y*z), > then > > > it > > > > > does > > > > > > > not divide (x+y)*(x+z)*(y+z), > > > > > > > > > > > > Why? > > > > > > > > > > > > If x = 4, y = 5, z = 7, for instance, then > > > > > > > > > > > > x + y is divisible by 3, which is > relatively > > > > prime > > > > > to > > > > > > xyz. > > > > > > > > > > Besides, 3 is also a divisor of another > factor > > > (y > > > > + > > > > > z). > > > > > > > > My couterexample above is not sufficient to > > > disprove > > > > your argument, since it can be easily shown by > > > > Fermat's Little Theorem and the counterexample > > to > > > > Fermat's Last Theorem that > > > > > > > > x + y = z mod 3; > > > > > > > > hence, if x + y is divisible by 3, then so is > z, > > > > contradictory to the first case assumption. > > > > > > > > However, I would like to present the following > > > > example: > > > > > > > > x = 7, y = 10, z = 47. > > > > > > > > x + y = 17 is not divisible by 3; > > > > > > > > x + z = 54 = 3*18; > > > > > > > > y + z = 57 = 3*19. > > > > > > > > I hope I did the arithmetic right. > > > > > > > > > > It is well established that a counter example > MUST > > > form a Triangle > > > > > > In my previous posts, I stated that a counter > > example > > > must form an integer triangle (with one side > only > > > even integer), and the largest angle between > > (PI/2, > > > PI/3) > > > > > > So, you see it follows directly > > > > > > Yours are not a counter example > > > > > > > > > Where is the previous post? > > > > > > > My Regards > > > > > > Bassam Karzeddin > > > AL Hussein bin Talal University > > > JORDAN > > You may see at the following link, even I may have > posted it befor > > http://mathforum.org/kb/message.jspa?messageID=4695333 > &tstart=0 So, should we focus on the validity of an argument in this old thread at this moment? > > My Regards > > Bassam Karzeddin
From: bassam king karzeddin on 27 Feb 2007 16:06 Hello Dear The theme is that I have realised that I have solved FLT, EVEN (16) YEARS BEFORE I KNEW ABOUT IT. YOU may wonder how!! IF S^P + M^P =L^P My turn is a formula for P Your turn is to know why it doesn't work for integers > 2 so, simple question after a formula is being found, but it was not suitable for them MANY YEARS BACK Now, I realised that somthing WRONG happeining world wise in the holly science-MATHEMATICS, AND, PYTHAGOURS, FERMAT, ...,ARE ALL very , very, VERY ANGRY THEN, WITH YOUR HELP, we are going to CHANGE THE RULES My Regards Bassam Karzeddin Al Hussein bin Talal University JORDAN
From: bassam king karzeddin on 27 Feb 2007 16:13
> > > > > Hello TO ALL > > > > > > > > > > The only remaining case -PROOF > > > > > > > > > > Now, you may easily derive the following > > > identity > > > > for > > > > > a counter example when (p) is a prime factor > > OF > > > > > (x*y*z) > > > > > > > > > > Let x^p + y^p = z^p, where (x,y,z) are three > > > > positive > > > > > coprime integers, then the following > identity > > > must > > > > > hold > > > > > > > > > > (x*y*z)^p = > > > (x+y)*(z-x)*(z-y)*N(x,y,z) > > > > > > > > > where > > > > > > > > > > > > > > Gcd((x+y)*(z-x)*(z-y), N(x,y,z))= p, > > > > > > > > > Very Simple to prove, (no need to waste time > > on > > > > > that) > > > > > > > > > > Now, (p^k*p) divides the left hand side of > the > > > > above > > > > > identity, where as p^(k*p-1) only divides > the > > > > right > > > > > hand side of the above Identity, where k is > > > > positive > > > > > integer number,and as I had shown you today > > from > > > > > other post. > > > > > > > > > > Therefore, the identity can't hold true with > > > > integer > > > > > numbers defined above AND THERE IS NO > COUNTER > > > > > EXAMPLE > > > > > > > > > > Hence THE PROOF IS INDEED COMPLETED > > > > > > > > SORRY, a flaw was found by me few hours after > > > posting > > > > proof of this case and it is no more valid, > but > > I > > > > have another one > > > > > > I will be happy to read another argument. > > > > > > > > > > > > You may add any suitable references, and > then > > > > write > > > > > it in any suitable languge, beside let the > > > > JOURNALS > > > > > KNOW ABOUT IT > > > > > > > > > > > > > > > > > > > > > > > > > > > > MY BEST REGARDS > > > > > > > > > > Bassam Karzeddin > > > > > > > > > > AL Hussein bin Talal University > > > > > > > > > > JORDAN > > > > I have already corrected that argument > > Actually, I had not even asked what the mistake was. Dear Hisanobu Shinya It was not leading to the result I desire, so, let it go... My Regards > > > > > B.Karzeddin |