The First Case of Fermat's Last Theorem is True for all Prime Exponents up to 714,591,416,091,389

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 1988Publisher:JSTORJournal:Transactions of the American Mathematical Society, volume 306, page 329 (issn: 0002-9947,

Copyright policy )

Authors: Granville, Andrew; Monagan, Michael B.;

doi: 10.2307/2000841 , 10.1090/s0002-9947-1988-0927694-5

The First Case of Fermat's Last Theorem is True for all Prime Exponents up to 714,591,416,091,389

- Summary
- Subjects
- Metrics

Abstract

We show that if the first case of Fermat’s Last Theorem is false for prime exponent p p then p 2 {p^2} divides q p − q {q^p} - q for all primes q ⩽ 8 q q \leqslant 8q . As a corollary we state the theorem of the title.

Related Organizations

University of Toronto
Canada
IBM (United States)
United States

Keywords

Pollaczek's work, Gunderson's function, Kummer-Mirimanoff congruences, Higher degree equations; Fermat's equation, first case of Fermat's last theorem

Impact byBIP!

	selected citations These citations are derived from selected sources. This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	15
	popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.	Average
	influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	Top 10%
	impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.	Average