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Maybe The Simple Explanation for Pythagorean Triples is the fact Power 2 for Integers T can be also writen in a linear mode.
T | |
∑ | [ (2I+1) |
I=0 |
X | Y | Z | ||||||
∑ | [ (2I+1) | + | ∑ | (2I+1) | = | ∑ | (2I+1) | |
I=0 | I=0 | I=0 |
Z | Y | |||||||
∑ | [ (2I+1) | + | ∑ | (2I+1) | = | 0 | ||
I=Z-X | I=0 |
Related to Fermat's Last Theorem and Pythagorean Triple, this form speak a lot now.
There are Integers(X, Y, Z) for which Fermat's Last Theorem have validity, and a lot for which it not (Pythagorean Triple). Those are EXCEPTIONS from Fermat's Last Theorem
which Confirm The RULE by explain in a sense it.It and a lot of mores motivations are including Pythagorean Triple into Fermat's Last Theorem as EXCEPTIONS.
An another motivationfor Magic Two Exception is Pythagorean Media or Geometric Media not as a Arithmetic Media.
Fo five Integers {A, B, Y, X, Z} there are Infinty of Conjectures
0 | |
∑ | [ (-1)m(k < sub > I sub >< sup > n sup >)(T+I)n]= n! |
I=n |
But, The "Power" of Magic 2 as Pythagorean Triples Exceptions of Fermat's Last Theorem is coming from:
Those are Properties for wich any 3 Integers Fermat's Last Theorem Exceptions, pass with validity Fermat Murgu n Media for 3 Integers, Fermat - Murgu Impossible Equations, and to reflect absolute all Integers into mirrored interval[0, 1 / 2]. (Including Pythagorean Primes, which can't to be Z, but for sue any X's or Y's.)
But The purest Mathematics explanation is simple- RELATIVE TO POWER, 2 PRESENT SYMMETRY WITH MULTIPLICATION.
It isn't a explanation of Fermat's Last Theorem, instead, is a logic explanation for what power 2 admit exceptions from.
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