Feit-Thompson conjecture

Conjecture (Walter Feit & John Thompson). There are no prime numbersMathworldPlanetmath p and q (with pq) such that pq-1p-1 is divisible by qp-1q-1.

Feit and Thompson, in regards to the Feit-Thompson theorem, have said that proving this conjecture would simplify their proof of their theorem, “rendering unnecessary the detailed use of generators and relations.” In 1971, Stephens strengthened the conjecture to state that


always, and then found the counterexample p=17, q=3313. The numbers 173313-117-1 and 331317-13313-1 do have 112643 as their greatest common divisorMathworldPlanetmathPlanetmath, but dividing the former by the latter leaves a remainder of 149073454345008273252753518779212742886488244343395482423. No other counterexamples have been found to Stephen’s stronger version of the conjecture.


Title Feit-Thompson conjecture
Canonical name FeitThompsonConjecture
Date of creation 2013-03-22 17:55:38
Last modified on 2013-03-22 17:55:38
Owner PrimeFan (13766)
Last modified by PrimeFan (13766)
Numerical id 8
Author PrimeFan (13766)
Entry type Conjecture
Classification msc 20A05
Classification msc 20E32