ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

3. Number Theory and Arithmetic Algebraic Geometry

1991 MS Classification: 1, 11 Griffiths, Peter L., Chartered Accountant, UK Fermat’s Last Theorem, a Simple Proof based on Irrational Numbers If n is an integer greater than 1 then the n-th root of all primes greater than 1 and of all irrationals is irrational. If t and n are integers greater than 1 then (t^{n} ± 1)^{1/n} will be irrational even when n = 2. (a^{n} + b^{n})^{1/n} is always irrational if n is greater than or equal to a which is greater than b which is greater than 1 (all being integers). This automatically excludes the Diophantine identity with n = 2. The notion of infinite descent comes from Diophantus’s use of the Greek word APEIRACWS meaning in an infinite number of ways.