Andrea Ossicini

• PhD in Mathematics and Engineering
• Researcher at My home

In this work, I provide a new rephrasing of Fermat's Last Theorem, based on an earlier work by Euler on the ternary quadratic forms. Effectively, Fermat's Last Theorem can be derived from an appropriate use of the concordant forms of Euler and from an equivalent ternary quadratic homogeneous Diophantine equation able to accommodate a solution of Fe...

Ramanujan-Jacobi in In Andrea Ossicini

In this work, I provide a new rephrasing of Fermat's Last Theorem, based on an earlier work by Euler on the ternary quadratic forms. Effectively, Fermat's Last Theorem can be derived from an appropriate use of the concordant forms of Euler and from an equivalent ternary quadratic homogeneous Diophantine equation able to accommodate a solution of Fe...

The Mathematics Editorial Office retracts the article entitled “On the Nature of Some Euler’s Double Equations Equivalent to Fermat’s Last Theorem [...]

An Additional Remarks on a Reformulation of Fermat's Lat Theorem

Update of Paper "On the Nature of Some Euler’s Double Equations Equivalent to Fermat’s Last Theorem"

In relation to the Expression of Concern published on May 29, 2024 by MDPI, see the paper "On the Nature of Some Euler's Double Equations Equivalent to Fermat's Last Theorem" the author (Andrea Ossicini) provided an update of his paper to adequately respond to the various objections, unfortunately (let's say incorrectly)it was not even considered.

1. The proof Ossicini's proof is based on a reductio ad absurdum. This study provides a new rephrasing of Fermat's theorem, based on Euler's earlier work on ternary quadratic forms, which in an indirect way provides a new proof of the Last Theorem

Fermat and his genius !!!

1. The proof Ossicini's proof is based on a reductio ad absurdum. This study provides a new rephrasing of Fermat's theorem, based on Euler's earlier work on ternary quadratic forms, which in an indirect way provides a new proof of the Last Theorem.

Fermat and his genius !!!

Artificial intelligence makes its entry into science

This work illustrates how determine the value of the parameter Q, present in the double Euler equations. classification : 11D41 (primary), 11G05 (secondary).

This work comment two papers: the first published in 2022 and entitled "On the nature of some Euler's double equations equivalent to Fermat's last theorem" provides a proof through the so-called discordant forms of appropriate Euler's double equations, which could have entered in a not very narrow margin and the second instead published in 2024 and...

"a remarkable integration between Fermat’s equation and Euler’s double equations".

This work illustrates how determine the value of the parameter Q, present in the double Euler equations. classification : 11D41 (primary), 11G05 (secondary).

In this work I demonstrate that a possible origin of the Frey elliptic curve derives from an appropriate use of the double equations of Diophantus-Fermat and from an isomorphism: a birational application between the double equations and an elliptic curve. From this origin I deduce a Fundamental Theorem which allows an exact reformulation of Fermat’...

In this work, I provide a new rephrasing of Fermat’s Last Theorem, based on an earlier work by Euler on the ternary quadratic forms.

385 (1637-2022) years later, Fermat's proof of his last theorem has finally been rediscovered.

In this work, I provide a new rephrasing of Fermat’s Last Theorem, based on an earlier work by Euler on the ternary quadratic forms. Effectively, Fermat’s Last Theorem can be derived from an appropriate use of the concordant forms of Euler and from an equivalent ternary quadratic homogeneous Diophantine equation able to accommodate a solution of Fe...

A wonderful Diophantine Equation that represents a remarkable integration between Fermat’s equation and Euler’s double equations.

A perfect reformulation of Fermat's Last Theorem

The equation (4), in tis paper, represents a extraordinary and "wonderful" integration between the equation of Fermat and Euler's double equations for the definition of one homogeneous quaternary Diophantus equation of the second degree not solvable in whole numbers.

The Fundamental Theorem and a Conjecture !!!

In this work, I provide a new rephrasing of Fermat’s Last Theorem, based on an earlier work by Euler on the ternary quadratic forms. Effectively, Fermat’s Last Theorem can be derived from an appropriate use of the concordant forms of Euler and from an equivalent ternary quadratic homogeneous Diophantine equation able to accommodate a solution of Fe...

In this work, I provide a new rephrasing of Fermat’s Last Theorem, based on an earlier work by Euler on the ternary quadratic forms. Effectively, Fermat’s Last Theorem can be derived from an appropriate use of the concordant forms of Euler and from an equivalent ternary quadratic homogeneous Diophantine equation able to accommodate a solution of Fe...

su Internet .. https://www.mdpi.com/2227-7390/10/23/4471/htm Articolo su Intennet https://www.mdpi.com/2227-7390/10/23/4471 Abstract su Internet

In this work, I provide a new rephrasing of Fermat’s Last Theorem, based on an earlier work by Euler on the ternary quadratic forms. Effectively, Fermat’s Last Theorem can be derived from an appropriate use of the concordant forms of Euler and from an equivalent ternary quadratic homogeneous Diophantine equation able to accommodate a solution of Fe...

In this work, I provide a new rephrasing of Fermat’s Last Theorem, based on an earlier work by Euler on the ternary quadratic forms. Effectively, Fermat’s Last Theorem can be derived from an appropriate use of the concordant forms of Euler and from an equivalent ternary quadratic homogeneous Diophantine equation able to accommodate a solution of Fe...

In this work, I provide a new rephrasing of Fermat’s Last Theorem, based on an earlier work by Euler on the ternary quadratic forms. Effectively, Fermat’s Last Theorem can be derived from an appropriate use of the concordant forms of Euler and from an equivalent ternary quadratic homogeneous Diophantine equation able to accommodate a solution of Fe...

However, we did not succeed, as in the "proof a' la Fermat ", documented and justified in this note to establish in more absolute way the non-existence of the Diophantine equation, ternary and homogeneous of the second degree, capable of accommodating one possible integer solution of Fermat's equation, but we have stated an equivalent Theorem, at l...

A third elementary proof of Fermat's Last Theorem

A Proof of non-existence of the second degree Dio-phantine equation, which includes a solution of Fermat's equation X^n+Y^n=Z^n.

The following appendix completes the definition of the integer parameter "h" in my elementary proof of Fermat's Last Theorem.

In this work I demonstrate that a possible origin of the Frey elliptic curve derives from an appropriate use of the double equations of Diophantus-Fermat and from an isomorphism: a birational application between the double equations and an elliptic curve. From this origin I deduce a Fundamental Theorem which allows an exact refor-mulation of Fermat...

Logic of Paper "The Diophantus's double equations equivalent to Frey's curve"

The following work furnishes a ”direct” proof of the so-called ”Fermat’s Last Theorem”, by using elementary techniques, related perhaps to thehistorical period going up to the 18th century. As we well know, Fermat’s LastTheorem was demonstrated in 1995 by the English mathematician A. Wiles, with the contribution of R. Taylor, through a ”reductio ad...

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Abstract. This paper treats about one of the most remarkable achievements by Riemann, that is the symmetric form of the functional equation for ζ(s). Riemann provides two different proofs of this. We present here, after showing the first one, a new, simple and direct proof of the symmetric form of the functional equation for both the Eulerian Zeta...

The goal of this manuscript to make clear what Fermat had in mind. By the use of the concordant forms of Euler and a homogeneous ternary quadratic Diophantine equation is certainly possible, also through methods known and discovered by Fermat,to solve its extraordinary Last Theorem.

This work contains two papers: the first entitled "On the nature of some Euler's double equations equivalent to of Fermat's last theorem" presents a marvellous proof through the so-called discordant forms of appropriate Euler's double equations, which could have entered in a not very narrow margin, i.e. in only a few pages (less than 14). The secon...

This work contains two papers: the first published in 2022 and entitled ”On the nature of some Euler’s double equations equivalent to Fermat’s last theorem” provides a marvellous proof through the so-called discordant forms of appropriate Euler’s double equations, which could have entered in a not very narrow margin and the second instead published...

REFERENCES for the Paper: THE LOST PROOF OF FERMAT'S LAST THEOREM.

This paper treats about one of the most remarkable achievements by Riemann, that is the symmetric form of the functional equation for ζ(s). We present here, after showing the first proof of Riemann, a new, simple and direct proof of the symmetric form of the functional equation for both the Eulerian Zeta function and the alternating Zeta function,...

This paper treats about one of the most remarkable achievements by Riemann, that is the symmetric form of the functional equation for ζ(s). Riemann provides two different proofs of this. We present here, after showing the first one, a new, simple and direct proof of the symmetric form of the functional equation for both the Eulerian Zeta function a...

For the first two Parts see [ibid. 27, 63–90 (2005; Zbl 1265.33010)] and [ibid. 29, 141–150 (2006; Zbl 1265.33011)].

In this paper we present a simple method for deriving an alternative form of the functional equation for Riemann's Zeta function. The connections between some functional equations obtained implicitly by Leonhard Euler in his work "Remarques sur un beau rapport entre les series des puissances tant directes que reciproques" in Memoires de l'Academie...

Nuovi Teoremi sui numeri primi e sui numeri naturali " Proposizione 1 1: ogni numero primo > 2 si può partizionare in un unico modo nella differenza di due quadrati di naturali. (1) () () m = m + 1 2 2 m-1 2 2 = m 1 con m = 2n + 1 ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ − ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ ⋅ ∈ N N La dimostrazione è conseguenza della (1) e del Teorema fondamentale dell'Aritmetica....

The purpose of the work is to furnish a complete study of a discrete and special function, discovered by the author and named with the Arabian letter "SHIN" {The letter SHIN is the thirteenth letter of the Arabian alphabet}. It includes three other papers, published in the International journal "Kragujevac Journal of Mathematics". The methods, the...

We describe a method for estimating the special function , in the complex cut plane A = C\ (−∞, 0], with a Stieltjes transform, which implies that the function is logarithmically completely monotonic. To be complete, we find a nearly exact integral representation. At the end, we also establish that 1/ (x) is a complete Bernstein function and we giv...

This Paper (one first and draft version) contains some small imperfections, one its correct and definitive version has been already submitted to one prestigious review of mathematics. More precisely "the Special Function SHIN, II" will be published in the "Kragujevac Journal of Mathematics, 29 (2006) ".

The purpose of the work is to furnish a complete study of a discrete and special function, discovered by the author and named with the Arabian letter "SHIN" {The letter SHIN is the thirteenth letter of the Arabian alphabet}. It includes three other papers, published in the International journal "Kragujevac Journal of Mathematics". The methods, the...

We prove the following exact symbolic formula of the special function Ä, in the entire s-complex plane with the negative real axis (including the origin) removed, with a double Laplace transform: Ä (s) = Lf 2 ¢ - (t) + Lf 1 2…i¢( Ä (t ¢ e ¡i…) ¡ Ä (t ¢ e i…))g g where - (t) stands for the distribution of Dirac and e represents the Euler's number.