Pierre de Fermat: differenze tra le versioni
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[[en:Pierre de Fermat]]
[[hu:Pierre de Fermat]]
The Fermat’s Last Theorem
Everyone is convinced, for example, that there is no direct proof of Fermat's Last Theorem (or FLT), whose wording is as follows:
"The diophantine equation
(F) xn + yn = zn admits no positive entire solutions for n>2 "
The reasons for this <conviction>?
L '<innocent> complicity of the media and two books of mathematics disclosure checked very appropriately and very soon opportunistically after the < indirect> proof of Fermat's Last Theorem (FLT) by the British mathematicians A. Wiles and R. Taylor, obtained in 1994 (19 September) following the demonstration <original and direct> of a variant of the conjecture Taniyama-Shimura (D-CT) (1955), published in May 1995, but confirmed only in 1998 by the International Mathematical Union.
"Coming into possession of a direct proof of the LFT was the <dream of dreams> all mathematicians for several centuries, starting from Euler (who had even inspected the house of Fermat in Toulouse!), to finish at the same Wiles , which - not being able to get over at least one quarter of a century, a direct proof of the LFT - it had to settle for an indirect demonstration of the LFT. "
(O. Gallo, The Enigma of Fermat's Last Theorem, 1996).
And here, for example, as was presented to the SIAE Rome 27.XII.1993 by Onofrio Gallo the memory Sulla risolubilità delle equazioni diofantee del tipo (F) xn + yn = zn ( On the solvability of the diophantine equations of type (F) xn + yn = zn ):
"The memory is composed of 6 (six) typewritten pages numbered and signed by the author. In them is exposed for the first time in the History of Mathematics the Fundamental Theorem of Gallo [then best known as Gallo’s Mirabilis Theorem] for the resolution of diophantine equations of the type (F) xn + yn = zn in terms of whole (positive). The Gallo’s Fundamental Theorem is also in the general case, the very first demonstration general "basic" and "constructive" in the so-called Fermat’s Last Theorem.
Research related to these results have been carried on since 1989 with regard to the Theory of Transformations of Identities in Equations, whereas the case n = 2 of this theory applied to the Pythagorean identity was published in 1991 (O.Gallo - "A new line in mathematical research: from identities to equations" on the mounthly of Sciences and Culture Oltre il 2000 (Beyond The 2000), n.1, oct. 1991, p. 4, Salerno, Italy) “
The keys of the first general direct proof by Mr. Prof. Onofrio Gallo of Fermat’s Last Theorem (or FLT) are two:
a) The Gallo’s Principle of Disidentity, discovered as part of its TTIE (or Theory of Transformations of Identities in Equations, 1989); a paradoxical principle (in the eyes of amazed <Euclidean geometers>) just received, albeit in a nebulous in certain respects from the same Cauchy in the applications of the theory of congruences of higher order created by Gauss and resumed later, in a new light, from L. Kronecker (1823 -1891) for a reduction into arthmetics of Mathematics: pushing the imaginary unit, as-according to him-
"All results of the most profound mathematical research should be able to express a view in the simple form of ownership of integers”;
b) The Second Principle of General Knowledge, F F= T , where F is a property <false or not exact>, an appropriate algorithm and T is a property exact or true, used since antiquity in many names and in various chapters of Mathematics and also as show below, unknowingly at the moment (19.09.1994) from the same Wiles, to demonstrate the validity of partial conjecture Taniyama-Shimura and the subsequent general indirect proof of the FLT.
In the three chapters of this short work we placed <innermost math’s harmonies > in the Theorem of Pythagoras, the Fermat's Last Theorem and the Mirabilis Theorem of Gallo that unifies them, and far exceeds them, not without a few paragraph irrationality in science and the most daring mathematical theory (developed from 1980 onwards) existing in the field of discrete random predictions of future events: the TMPECF by O. Gallo.
Onofrio Gallo (brief bio-bibliographical note )
Italian mathematician born May 13 1946 in Cervinara (Avellino) (Valle Caudina).
He studied in Maracaibo (Venezuela) (College “L Gonzaga "Jesuit fathers), in Pozzuoli (Naples) (College of the Archbishop 'S. Paul"), in Maddaloni (Caserta) (Convitto Nazionale "G. Bruno"), in Naples (Liceo Scientifico Statale "V. Cuoco"), in Naples (University "Federico II", including a Masters in Mathematics (at the Faculty of Sciences) with an original thesis in Abstract Algebra (Sui quasigruppi commutativi, mediali, idempotenti) , then specializing in theories and techniques for the use and application of computers in the Faculty of Engineering and attending, post graduate, the School of PhD in Theoretical Physics and Nuclear (Mostra d'Oltremare), attached to the Faculty of Physics same university ..
Works in mathematics: the unplublished treaty Mathemantics (1980-2005)(on the prediction of <single> future discrete random events); in the Number Theory the unplublished Treaty on diophantine equations (1995), in which appears the Gallo’s Fundamental Theorem FPG / N on the Generalizated Fermat-Pell equations of degree k ≥ 2.
Over thirty articles published and the original core and fundamental memories:
Sulla risolubilità delle equazioni diofantee del tipo (F) xn+yn=zn (On the solvability of the diophantine equations (F) xn + yn = zn (Gallo’s Mirabilis Theorem) (Rome, 1993,)
Sur la résolubilté des équations du type de Diophante (F) xn + yn = zn (Gottingen, 1994)
New <Disquisitiones> On The Number Theory (Oslo, 2004)
From The Fermat's Last Theorem To The Riemann's Hypothesis (Oslo, 2004)
The Riemann-Gallo's Theorem (Oslo, 2004) on the equivalence of the infinite zeros of complex Gallo’s function ψ (psi) (real part = 1) and the infinite zeros of the Riemann’s Ϛ (zeta) function (real part = 1/2).
Original and general resolutions of its known and difficult mathematical problems, such as the Cattle’s Problem of Archimedes (in 1995), resolved on the basis of his Theorem FPG / N (which, after nearly three millennia, is used to calculate the k- nth root of any positive integer N (with N≠ nk and n positive integers) has resolved in various ways, providing <minima> diophantine solutions unknown to his predecessors, even when it is necessary to take account of new and difficult conditions (conditions of Gallo).
Even the well-known Problem of the sailors and coconuts has been solved by him, for the first time in the world, including in the general case using the <formulas Gallo>, without solving any diophantine equation!
Onofrio Gallo has developed several original and important <new> chapters of Mathematics, as TTIE or The Theory of the Transformations of the Identities in Equations (1989), The Theory of p-diophantine equations, The Theory of Generalized Fermat-Pell equations, The Theory of Random Hermitian Structures of order 3, The Theory of the ψ (psi)function.
On the basis of his Theory of p- diophantine equations the same Gallo has created the Theory of prime numbers of Gallo (of class even or of class odd of degree m) in the field of complex numbers and, for the first time in the history of mathematics, after about four thousand years, has succeeded in breaking the atoms of mathematics (the prime numbers p) in the product of two factors other than 1 and p.
In such theory a number p is a Gallo’s prime number of first species and even class if, and only if, it is the harmonic mean of the so-called Gallo’s harmonic numbers h e k (complex conjugates).
In other words p is a Gallo’s prime number, if, and only if, it is p = 2hk / (h + k), with h = 1-yi and k = 1+yi + yi, where i is the imaginary unit.
Generalizing the Theorem of Gallo (1994) on the proof of the Goldbach’s conjecture on the Goldbach’s prime numbers (solutions of the Goldbach’s equation p1 + p2 = 2n, with n> 2 and pr (r=1,2) prime numbers) for the powers more than 1 of Goldbach’s prime numbers (associated with Generalized equations of Gallo-Goldbach which are of type (GB/2n) pm1+ pm2 =2n (of even class) and (GB/2n +1) pm1+ pm2 = 2n +1 (of odd class) and with m ≥2 and n> 2) you can obtain infinite Gallo’s prime number of even class or of odd class of degree m.
Thus, while physicists were able to split the atom in the years'20-'30 of the twentieth century, mathematicians had to wait for over half a century (until 1994) to project beyond the Pillars of Hercules dating back at least the divisibility up to Euclid.
The new theory of Gallo’s prime numbers allowed, on the one hand to extend (an attempt failed by the same K.F.Gauss) in the field of complex numbers, the so-called f
Fundamental theorem of arithmetic (which allows to obtain an identikit of any positive integer) and, secondly, to develop a mathematical theory (the Theory of the function ψ (psi) of Gallo) parallel to Theory of the function Ϛ (zeta) of Riemann.
Through the function ψ of Gallo is possible to clarify the famous Riemann’s hypothesis about complex zeros of the complex zeta function, according to which
"all the complex zeros of the Riemann’s zeta function have real part on the line x = 1 / 2".
Assumption that mathematicians still failed to explain using the same zeta function.
Indeed there is a general demonstration of why this happens, despite the search for a counterexample made with the most powerful computer available.
The computer has demonstrated the validity of the assumption of Riemann for billion cases, but this is not sufficient for a general demonstration of the same.
The consequences? For the complex zeros of the Riemann’s zeta function do not know the real value of the coefficient y of the imaginary, but, as Riemann has suggested, these zeros have their real part x = 1 / 2.
A comparison between the complex zeros of the Gallo’sfunction psi and the Riemann’s zeta function shows that the complex zeros of the Gallo’s psi function is h = x-yi and k = x + yi with h, k Gallo’s harmonic numbers (ie p = 2hk / (h + k) with p prime) such that x=1 and y = √ (p-1) with p prime number, while for the complex zeros z = x + yi of the Riemann’s zeta function x = 1 / 2 (Riemann’s Hypothesis), and y is unknown a priori.
Onofrio Gallo has settled, after some four millennia, so comprehensive and definitive, and the problem of the calculation of primitive Pythagorean terns (Gallo’s General Theorem on Primitive Pythagorean Terns, 1994), as well as chapters on the problems of squares congruenti ( PSC) and the problems of the area-congruo numbers (PAC), dating back to Arab mathematicians, to Italian Magistri of Abaco and at the same Fibonacci.
Its also the first general and original world direct proof of Fermat's Last Theorem (FLT) (Rome, 1993; Gottingen 1994).
Its also the first general and original proofs of the Goldbach conjecture (1994) and the Conjecture of twin primes (1994), unpublished.
The FLT is the general case of his Mirabilis Theorem that, for the first time in the history of mathematics, to solve for symmetry (without trial and without radicals and without the use of continued fractions) diophantine and algebraic equations of any degree n (finished), the problems solved by Ramanujan with the use of continued fractions and, for n = 2, to calculate –over Pythagoras- two sides of a right triangle, known only the third side , <to unify>, for the first time in Mathematics, the discrete with continuous and to solve many other difficult problems.
Its Non Standard Theory of Transformations of Identity in Equations (1989) go beyond Euclid and logical principles and semi-logical underpinning of his fundamental unpublished treatise Mathemantics (or TMPECF or Mathematical Theory for the Forecast of Future Random Events; NP = not probabilistic and NQ = not qualitative), defined by some <the fourth scientific revolution of our times>.
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