A VARIANT OF THE PROOF OF THE FERMAT LAST THEOREM.
Keywords:
Fermat last theorem, Intermediate value theorem, increasing function, decreasing function, 2010 Mathematics Subject Classification, 11 A xx (Elementary Number theory)Abstract
In the 13 pages paper [7] published by the GJAETS, I have given a short elementary proof of the Fermat’s last theorem based essentially on the intermediate value theorem, the B. Bolzano (1781-1848)-K. Weierstrass (1815- 1897) theorem and the L. Euler (1707-1783)-J.C.F. Gauss (1777-1855) theorem . I have deduced the Fermat last theorem in my paper [8] resolving affirmatively the Beal conjecture and in my paper [9] resolving affirmatively the abc-conjecture. The two papers being published by the GJAETS in February 2021 and February 2022 respectively. In the present paper I give also another shorter elementary proof of this conjecture based only on the intermediate value theorem and the increasing properties of some elementary functions, using some techniques of my previous papers [5], [6], [8] and [9]. Recall that the hard problem of finding an elementary proof of this famous conjecture (called the Fermat last theorem), saying that the Diophantine equation
