As respect for Euler work and his intuition connected to Fermat's Last Theorem
(as I know him failed to demonstrate for n=3 all solutions are Irrational), I named a part of My work:
Euler Murgu Equations 1=1
Euler Murgu Equations 1=1 - is related to Fermat Equations and have validity for n>2 .
Fermat - Murgu Impossible Equations CERTIFIED Fermat's Last Theorem, sent it in Fundamental and brought Pythagorean Triple as exceptions from Fermat's Last Theorem
revealing also every Pythagorean Triple have a image in Irrational Field and Rational Field also. In fact we can speak about a evolving Irrational - Rational - Integers and inverse one.
And it have absolute validity for Pythagorean Triple , To take an example the triple {9,16,25}, base solution, {3,4,5}, this is the image into Integers , in Rational field is {9/25,16/25,1}, base solution {3/5,4/5,1}, for Irrational Field I will say without more work on
{ (9/25 √2), (8 √2/25), 1/√2 }, base solution maybe { (3 √2 /5), (8/5 √2),(1 √2) } . Out of our appetity for simplfy, any times
can lay any sense into, so those are values which satisfy X2 + Y2 = Z2 .
To name Fermat's Last Theorem Equation General Cases , Fermat Equations,
Xn + Yn = Zn
To divide it with Zn , and to name with :
A=Xn/Zn and B=Yn/Zn
Then will get:
A+B=1 WITH A and B under unity values and both Rationals or Irrational. I HOPE DON'T NEED A POSTULATE A IRRATIONAL NUMBER CAN'T BE COMPENSATED TO UNITY
BY another kind then another Irrational and relative to sum its Complementary to UNITY.
As already know FMIE brought all Solutions Bases for Fermat Equations in Irrational , even if X,Y or Z (one of it)
is Integer , then 2 of Them Irrational. Even Pythagorean triple are strting from there.
Then, to consider the case, and to write it as:
A + (1-A) = 1
Euler - Murgu Equations - its simple beauty here.
Euler - Murgu Equation 1=1 contain hiden, a SOLUTION FOR Fermat's Last Theorem, and hide by DOUBLE FALSE REDUNDANCY OF TRUTH.
For special Irrational Numbers, n√n , which evolve to n , only by n times proper multiply,
A + (1-A) = 1
never(EXCLUDING n=2 EXCEPTIONS explained) will evolve to an Integer.
Now, a problem yet stand up for rezolving. Is n√n a IRRATIONAL NUMBER FOR EVERY n's? It is because cleary every Prime Number P of form
P√P will evolve tp P - INTEGER, ONLY BY P-TIMES MULTIPLY WITH ITSELF, and the rest are combinations of prime numbers. In those combinations , every time
related to n, at the last one factor will not have parity to n.
- For sure Euler - Murgu Equations will get the PLACE in Physics in conservations processes with entropic comportaments.
By here is a simple Algebraic case , which need a simple Explanation:
We know From Fermat-Murgu Second Grade Impossible Equations, solutions are of form - for n=2 (X - X√2) , for n =3 (X - X∛3), for n =4 (X - X∜4) and so on (X- X n√ n),
then A can be transfered into Integer by multiply (n-1√n) . But By doing it, is simple to see (1-A) became Irrational, and we are in a redundancy of
ABSURD.
Euler - Murgu Equations 1=1 , also CERTIFY Fermat's Last Theorem, but FMIE remain The method Which sent it in Fundamental.
FMIE sent all base solutions for in irrational.
© 2015 - for: Ion Murgu Integers Powers Fundamental Equations, Fermat's Last Theorem Fundamental,Fermat-Murgu Impossibe Equations, Fermat-Murgu Quadruplets, Euler - Murgu Equations 1=1 .
∜ ∛
