AMERICA EARTH PROUD DAY FUNDAMENTALS

THE LOST FUNDAMENTAL sent
Fermat's Last Theorem - FUNDAMENTAL

THE LOST FUNDAMENTAL

or Ion Murgu - Integers Powers Fundamental Equations.

The fundamental which via FMIE sent Fermat's Last Theorem in - FUNDAMENTAL

HUMANITY SCINECE THESAURUS

those equations not only lightened near of 400 years of research about - Fermat's Last Theorem , but brought a lot more.

Ion Murgu - Integers Powers Fundamental Equations.

GETTING FORMULA

What been waiting for is proved, as remark I did it for n=2, n=3, n=4, n=5, n=6 and n=7, then not a motivation to exclude general case, and late on I make a software which proved it for n between 1 and 50. Then, I made second STEP, to get The Formula, and for it I keept the powers from first row as functions of I and n. We will do it for n=4, for general case is heavy to make a schema, but as I said a Software ( a PERL script will proved it, and is on Internet already by a long time )

For general cases a Table will be To big , but an atempt can be made(I did) needed to see the Evolving Coefficients (Pascal Triangle). A Computing form is a easy procedure, because every superiors Coefficients are evolving also from the precedents.

Now we have Formula in the front of us in two forms.

THOSE INFINITY TO INFINITY EQUATION - IDENTITIES ARE IMPORTANT FOR , BECAUSE EXPRES ABSOLUTE TRUTH . EVEN PRIME NUMBERS GET NOW THE CONNECTION WITH ALL NUMBERS ON.

THOSE INFINITY TO INFINITY EQUATION - IDENTITIES I HAD the dare, with your permission, to name - HUMANITY SCIENCE THESAURUS - . And it, not because I get it, but because are. Are simple now, but we needed 7000 years of Scince to get it. To not confuse it whith Pascal Equations what been obtained by simple evolving of (a+b)ⁿ by multiple multiply of (a+b)... (a+b). Here we get the real conection whth n!. In first place, I named THOSE INFINITY TO INFINITY EQUATION - IDENTITIES as ION MURGU - MATH MILLENIUM EQUATIONS as a remark we get at the begin of Millennium any important aproach, but late, I renamed it ION MURGU - INTEGERS POWERS FUNDAMENTAL EQUATIONS - TO REMARK THE RIGHT TO fundamental.

Ion Murgu- Integers Powers Equqtions will play a role in Numbers Theory

Via Ion Murgu- Integers Powers Equations, Prime Numbers can be wrie now in multiple forms.
Polinomial function also.
Those equations are valids for T Integer >n , and it expose the same problem which appear in Complex Numbers , see Riemann hypotesis.
Those equations EXPRES - ABSSOLUTE TRUTH, AND CAN BE TESTED BY 2 YEARS AND THE HALF at : www.lifeclimatic.com/mmc.pl , and now under this software. Ion Murgu Integers Powers Fundamental Equation present also a impass of interfernce on all Integers Axes , and is coming from desechilbre introduced by interval [-1,1],which in Riemann Hypotesios wear anyher aspect by refleted. FORMULA for Ion Murgu Integers Powers Equations working on Intervales [-1,∞] and [1,∞] is down:

0
∑	[ (-1)m(kI,n)(B+I)n]
I=n

Diference is "m" will be m=(I+1) for n par , and m=I for n odd

As you will see: Ion Murgu Integers Powers Fundamental Equations can CERTIFY Fermat's Last Theorem , VIA an Analytic Math Method named, maybe improper, Fermat-Murgu Impossible Equations. Ion Murgu Integers Powers Fundamental Equations lighted totally Fermat's Last Theorem , Generalize it by sending all Fermat Equations Solutions Into Irrational Field