CONFIRMATION OF THE ABC-CONJECTURE AND DEDUCTION OF SOME CONSEQUENCES
Keywords:
abc- conjecture, Intermediate value theorem, L’Hôpital rule, Increasing function, decreasing functions, Extremums, Fermat last theorem, The Beal conjecture, The Roth theorem, The Fermat/Catalan conjecture, The Wieferich/Silverman theorem, The Erdos/Woods conjecture, 2010 Mathematics Subject Classification, 11 A xx (Elementary Number theory)Abstract
I confirm, in the present short note, the famous abc-conjecture, remained open since 1985 and described by Dorian Goldfeld in 1996 (See [43]) to be « the most important unsolved problem in Diophantine analysis », by using elementary tools of mathematics such as the intermediate value theorem, the L’Hôpital rule and the growth properties of some elementary functions. Various attempts to prove the conjecture have been made, but none are currently accepted by the main Stream mathematical community such as the very long-in 600 pages- proof [71] by the Japanese Mathematician Schinichi Mochizuki (Born in March 29, 1969)-published in 8/2012- declared- by Peter Sholze and Jacob Stix in september 2018- that it « is, in state, not receivable » (See [91]). Some important consequences, such as the Fermat last theorem, the Beal conjecture, the Roth theorem, the Fermat-Catalan conjecture, the Wieferich-Silverman theorem, the Erdos-Woods conjecture…, are deduced.
