Very Original Proofs of Two Famous Problems: “Are There Any Odd Perfect Numbers?” (Unsolved until to Date) and “Fermat’s Last Theorem: ANew Proof of Theorem (Less than One and a Half Pages) and Its Generalization

Por • 2 may, 2022 • Sección: Opinion

Demetrius Chr. Poulkas

Abstract This article presents very original and relatively brief or very brief proofs about of two famous problems: 1) Are there any odd perfect numbers? and 2) “Fermat’s last theorem: A new proof of theorem and its generalization”. They are achieved with elementary mathematics. This is why these proofs can be easily understood by any mathematician or anyone who knows basic mathematics. Note that, in both problems, proof by contradiction was used as a method of proof. The first of the two problems to date has not been resolved. Its proof is completely original and was not based on the work of other researchers. On the contrary, it was based on a simple observation that all natural divisors of a positive integer appear in pairs. The aim of the first work is to solve one of the unsolved, for many years, problems of the mathematics which belong to the field of number theory. I believe that if the present proof is recognized by the mathematical community, it may signal a different way of solving unsolved problems. For the second problem, it is very important the fact that it is generalized to an arbitrarily large number of variables. This generalization is essentially a new theorem in the field of the number theory. To the classical problem, two solutions are given, which are presented in the chronological order in which they were achieved. Note that the second solution is very short and does not exceed one and a half pages. This leads me to believe that Fermat, as a great mathematician was not lying and that he had probably solved the problem, as he stated in his historic its letter, with a correspondingly brief solution. To win the bet on the question of whether Fermat was telling truth or lying, go immediately to the end of this article before the General Conclusions.

Keywords Perfect NumbersOdd Perfect NumbersFermat’s Last TheoremGeneralization of the Fermat’s Last TheoremPrime Number ProblemsMillennium Problems

Share and Cite: Poulkas, D. (2021) Very Original Proofs of Two Famous Problems: “Are There Any Odd Perfect Numbers?” (Unsolved until to Date) and “Fermat’s Last Theorem: A New Proof of Theorem (Less than One and a Half Pages) and Its Generalization”. Advances in Pure Mathematics, 11, 891-928. doi: 10.4236/apm.2021.1111058.

Demetrius Chr. Poulkas1,2,3,4

1Department of Mathematics, Aristotle University of Thessaloniki, Thessaloniki, Greece.
2School of Electrical and Computer Engineering, National Technical University of Athens, Athens, Greece.
3School of the Faculty of Engineering, Aristotle University of Thessaloniki, Thessaloniki, Greece.
4Department of Mechanical Engineering and Aeronautics, Faculty of Engineering, University of Patras, Patra, Greece.
DOI: 10.4236/apm.2021.1111058   PDF   HTML   XML   138 Downloads   774 Views 

https://www.scirp.org/journal/paperinformation.aspx?paperid=113337

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