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Automorphic Function And Fermat's Last Theorem (3) (Fermat's Proof of FLT)
| Content Provider | Semantic Scholar |
|---|---|
| Author | Jiang, Chun-Xuan |
| Copyright Year | 2010 |
| Abstract | In 1637 Fermat wrote: “It is impossible to separate a cube into two cubes, or a biquadrate into two biquadrates, or in general any power higher than the second into powers of like degree: I have discovered a truly marvelous proof, which this margin is too small to contain.” This means: ( 2) n n n x y z n + = > has no integer solutions, all different from 0(i.e., it has only the trivial solution, where one of the integers is equal to 0). It has been called Fermat’s last theorem (FLT). It suffices to prove FLT for exponent 4 and every prime exponent P . Fermat proved FLT for exponent 4. Euler proved FLT for exponent 3. In this paper using automorphic functions we prove FLT for exponents 4P and P , where P is an odd prime. We rediscover the Fermat proof. The proof of FLT must be direct. But indirect proof of FLT is disbelieving. In 1974 Jiang found out Euler formula of the cyclotomic real numbers in the cyclotomic fields 4 1 4 1 1 1 exp m m i i i i i i t J S J − − = = ⎛ ⎞ = ⎜ ⎟ ⎝ ⎠ ∑ ∑ , (1) where J denotes a 4m th root of unity, 4 1 m J = , m=1,2,3,..., i t are the real numbers. i S is called the automorphic functions(complex hyperbolic functions) of order 4m with 4 1 m − variables [2,5,7]. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://mrelativity.net/Papers/45/auto_3_.pdf |
| Alternate Webpage(s) | http://vixra.org/pdf/1012.0009v3.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
