FERMATS LAST THEOREM PROVED BY INDUCTION accompanied by

FERMAT’S LAST THEOREM PROVED BY INDUCTION (accompanied by a philosophical comment)

Vasil Penchev Bulgarian Academy of Sciences: Institute for the Study of Societies and Knowledge: Dept of Logical Systems and Models vasildinev@gmail. com 13 Oct 2019 Sofia Seminar of “Logical Systems and Models”

The proof in detail I The contemporary formulation of Fermat’s last theorem (FLT) II All means necessary and sufficient for the proof III The general idea and scheme of the proof IV The modified modus tollens V Fermat’s infinite descent modified for the proof VI The enumerated series of modus tollens VII The derivative series of implications VIII The proof of FLT by induction

I The contemporary formulation of Fermat’s last theorem (FLT) •

II All means necessary and sufficient for the proof •

III The general idea and scheme of the proof •

III The general idea and scheme of the proof •

IV The modified modus tollens •

V Fermat’s infinite descent modified for the proof •

VI The enumerated series of modus tollens •

VII The derivative series of implications •

“FLT decomposed by the derivative series of implications” = “FLT proved by indiction” •

Appendix

Fermat’s last theorem proved by induction Fermat’s last theorem is proved elementarily for first (or second? ) time for 382 years: since 1647 when Fermat formulated it and perhaps proved it

The text published in Internet (e. g. in Phil. Sci Arhive)

The proof in the slides and that in Phil. Sci Arhive are slightly different Two slides (which follow) can describe the difference. They are according to the version in Phil. Sci and should be compared with the corresponding slides above

II All means necessary and sufficient for the proof •

III The general idea and scheme of the proof •