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The proof of Fermat's Last Theorem

✍ Scribed by Wong Chiaho

Publisher
Springer
Year
1996
Tongue
English
Weight
306 KB
Volume
17
Category
Article
ISSN
0253-4827

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✦ Synopsis

i) Instead of x~-l-y'=z "" we use (x -b)"-t-x" = (x-H-a)" (O. 1 ) as the general equation of Fermat's Last Theorem (FLT), where a and b are two arbitrary natural numbers. B)' means of binomial expansion, (0_1) can be written as n ~._ ~ (~)~,-~[a,_(2b),]=o (0.2) r= 1 Because a"--(-b ) ~ alwa)'s contains a+b as its factor, (0.2) Can be written as where Β’,=[a~--(-b)~]/(a-Jvb ) are integers for r =1,2,3 ..... n (ii) Lets be a.factor of a+b and let (a+b)=sc. We can use x=sy to transform (0.3) to the following (0.4) 11--2 (r)(Sv) -Β’,-k'~"JΒ’,-i r=l (iii) Dividing (0.4) by s ~-we have r= 1

On the left side of (0.5) there is a polynomial of y with integer coefficients and on the right side there is a constant c_~/s. If cΒ’/s is not an integer, then we cannot find an integer y to satisfy (0.5), and then FLT is true for"this case. I]" cq~,,/s is an integer, lt:e may change a and e such the cΒ’./sva an integer_

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