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- W3154667255 abstract "In a previous paper (https://dx.doi.org/10.2139/ssrn.3648127 ), I have demonstrated an elementary and thoroughly arithmetical proof of Fermat’s last theorem by induction if the case for “n = 3” is granted as proved only arithmetically (a fact a long time ago). Now the same case of “n=3” is inferred as a corollary from the Kochen and Specker theorem (1968): the eventual validity of Fermat’s equation would correspond to an admissible disjunctive division of a qubit into two absolutely independent parts therefore versus the contextuality of any qubit, implied by the Kochen –Specker theorem. The proof involves set theory, but only within the case “n=3” and implicitly, within any next levels of “n”. Thus the application of set theory and arithmetic can remain disjunctively divided as well: set theory, “locally”, within any level; and arithmetic, “globally”, to all levels. Thus, the relevance of Yablo’s paradox to the statement of Fermat’s last theorem is avoided. However, the mathematical structure relevant to the proof cannot be restricted to Peano arithmetic but to a generalized structure called “Hilbert arithmetic” and discussed in detail in another previous paper (https://dx.doi.org/10.2139/ssrn.3656179 ). Furthermore, Fermat’s last theorem in virtue of that kind of proof can be considered as another expression of Gleason’s theorem in quantum mechanics (or vice versa): the exclusions about (n = 1, 2) in both theorems as well as the validity for all the rest values of “n” can be unified after the theory of quantum information: the availability (respectively, non-availability) of solutions of Fermat’s equation can be proved as equivalent the non-availability (respectively, availability) of a single probabilistic measure as to Gleason’s theorem." @default.
- W3154667255 created "2021-04-26" @default.
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- W3154667255 date "2021-02-15" @default.
- W3154667255 modified "2023-09-26" @default.
- W3154667255 title "Fermat’s last theorem proved by the Kochen – Specker theorem and induction. The quantum-information unification of Fermat’s last theorem and Gleason’s theorem" @default.
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