Fermat‘s Last Theorem
Fermat‘s last theorem (proofed by Andrew Wiles in 1994)
a^(i) – b^(i) <> c^(i) a, b, c, i are elements of N with a > b, i >1, i<>2; a, b, c are coprime.
I) We start the proof with exponent i=3
If a³ – b³ = c³ then:
c³ = p1³ * p2³ * …
We name the primefactors p1 * p2 * p3 … prime factorbases P(c) of c:
P(c) = p1 * p2 * p3 …
We get:
a³ – b³ = P(c)³
For a³ = P(c)³ + b³ we get the condition
a³ mod (c+b) = 0 (c+b) is a divisor of a³
a³ mod (P(c) + b) <> 0 (P(c) + b) is no divisor of a³
because a, b and P(c) are coprime , therefor (P(c) + b) is coprime a³
As a result we get:
a³ – b³ <> P(c)³
and
a³ – b³ <> c³
If the proof is correct, it would also be correct for i>3.