In mathematics, the FeitThompson conjecture is a conjecture in number theory, suggested by Walter Feit & John G. Thompson (1962). The conjecture states that there are no distinct prime numbers p and q for which
If the conjecture were true, it would greatly simplify the final chapter of the proof (Feit & Thompson 1963) of the FeitThompson theorem that every finite group of odd order is solvable. A stronger (and rather implausible) conjecture that the two numbers are always coprime was disproved by Stephens (1971) with the counterexample p = 17 and q = 3313 with common factor 2pq + 1 = 112643. Informal probability arguments suggest that the "expected" number of counterexamples to the FeitThompson conjecture is very close to 0, suggesting that the FeitThompson conjecture is likely to be true. See also * Cyclotomic polynomials Links * Eric W. Weisstein, FeitThompson Conjecture at MathWorld. References * Feit, Walter & Thompson, John G. (1962), "A solvability criterion for finite groups and some consequences", Proc. Nat. Acad. Sci. U.S.A. 48: 968–970, <http://links.jstor.org/sici?sici=00278424%2819620615%2948%3A6%3C968%3AASCFFG%3E2.0.CO%3B2Q> MR0143802 * Feit, Walter & Thompson, John G. (1963), "Solvability of groups of odd order", Pacific J. Math. 13: 775–1029, ISSN 00308730 MR0166261 * Stephens, Nelson M. (1971), "On the FeitThompson conjecture", Math. Comp. 25: 625, ISSN 00255718, <http://links.jstor.org/sici?sici=00255718%28197107%2925%3A115%3C625%3AOTFC%3E2.0.CO%3B2H> MR0297686 Retrieved from "http://en.wikipedia.org/" 
