Fermat's Last theorem short proof
in [Math]
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From: bassam king karzeddin on 11 Apr 2007 00:16 > On Wed, 21 Feb 2007 09:51:51 EST, bassam king > karzeddin > <bassam(a)ahu.edu.jo> wrote: > > >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 > in fact N(x,y,z) is homogeneous in Z[X,Y,Z] and > d°=p-3 > > Lamé (1839) and Wells (1986) have used this equation > n to prove Fermat > for n=7 > > and this equation is used by ....James Harris Did they use it the same way I did? Regards B.Karzeddin > >(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 > > > >(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), > >So the above equation does not have solution > >(That is by dividing both sides by 3, you get 9 > times an integer equal to an integer which is not > divisible by 3, which of course is impossible > >I think proof is completed for (p=3, and 3 is not a > factor of (x*y*z) > > > >My question to the specialist, is my proof a new > one, more over I will not feel strange if this was > known few centuries back > > > >Thanking you a lot > > > >Bassam King Karzeddin > >Al-Hussein Bin Talal University > >JORDAN >
From: AP on 12 Apr 2007 09:13 On Wed, 11 Apr 2007 04:16:55 EDT, bassam king karzeddin <bassam(a)ahu.edu.jo> wrote: >> On Wed, 21 Feb 2007 09:51:51 EST, bassam king >> karzeddin >> <bassam(a)ahu.edu.jo> wrote: >> >> >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 >> in fact N(x,y,z) is homogeneous in Z[X,Y,Z] and >> d�=p-3 >> >> Lam� (1839) and Wells (1986) have used this equation >> n to prove Fermat >> for n=7 >> >> and this equation is used by ....James Harris > >Did they use it the same way I did? > I don't know for J H see a lot of messages on this group since 1999 (his adress www of 1999 is not valid)
From: William C Waterhouse on 12 Apr 2007 17:46 In article <24975251.1176279446561.JavaMail.jakarta(a)nitrogen.mathforum.org>, bassam king karzeddin <bassam(a)ahu.edu.jo> writes: >... > > >(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 > > > > > >(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), > > >So the above equation does not have solution > > >(That is by dividing both sides by 3, you get 9 > > times an integer equal to an integer which is not > > divisible by 3, which of course is impossible > > >I think proof is completed for (p=3, and 3 is not a > > factor of (x*y*z) >... The gap in the argument is in the marked lines. For instance, 3 does not divide 1*2*7, but it does divide (1+2)*(1+7)*(2+7). William C. Waterhouse Penn State
From: bassam king karzeddin on 17 Apr 2007 06:03 > On Wed, 11 Apr 2007 04:16:55 EDT, bassam king > karzeddin > <bassam(a)ahu.edu.jo> wrote: > > >> On Wed, 21 Feb 2007 09:51:51 EST, bassam king > >> karzeddin > >> <bassam(a)ahu.edu.jo> wrote: > >> > >> >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 > >> in fact N(x,y,z) is homogeneous in Z[X,Y,Z] and > >> d°=p-3 > >> > >> Lamé (1839) and Wells (1986) have used this > equation > >> n to prove Fermat > >> for n=7 > >> > >> and this equation is used by ....James Harris > > > >Did they use it the same way I did? > > > I don't know > for J H see > > a lot of messages on this group since 1999 > (his adress www of 1999 is not valid) I have read something of what J.H had been writing, but it seems to me like brain washing, may be he or some one else can explain us the link to this issue, and you are also welcomed to add any other real able links, preferably accessible on the internet and free of cost. I'm also preparing a very surprised material for you all, but unfortunately, and due to the very LITTLE time available for me to work in mathematics, they will be coming after some time Regards B.Karzeddin
From: bassam king karzeddin on 19 Apr 2007 05:36
Dear All As a generalization to one of my posts in this thread Given, two distinct, coprime non zero integers (x & y), Theorem- (new or old, I don't care), precisely I don't know If, (n & m) are two positive integers, where m = gcd ((x+y), n), then this implies the following theorem: Gcd ((x+y), (x^n+y^n)/(x+y)) = Rad (m), Where Rad (m) equals the product of all the prime factors of (m), that is to say Rad (m) is square free number that divides (x^n+y^n), or simply that proves FLT and some other unsolved problems if you can see, but unfortunately I don't have much time to show you the little dirty and silly work (the proofs), but it is still too easy to prove the above theorem, isn't it? Good Luck Regards بسام غرزالدين Bassam Karzeddin Al Hussein bin Talal University JORDAN |