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arguments suggest that the "expected" number of counterexamples to the Feit–Thompson conjecture is very close to 0, suggesting that the Feit–Thompson conjecture is likely to be true.
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475:(This article confuses the Feit–Thompson conjecture with the stronger disproved conjecture mentioned above.)
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Feit, Walter; Thompson, John G. (1962), "A solvability criterion for finite groups and some consequences",
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If the conjecture were true, it would greatly simplify the final chapter of the
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Le, Mao Hua (2012), "A divisibility problem concerning group theory",
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Stephens, Nelson M. (1971), "On the Feit–Thompson conjecture",
189:. A stronger conjecture that the two numbers are always
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47:). The conjecture states that there are no distinct
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219:It is known that the conjecture is true for
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331:Feit, Walter; Thompson, John G. (1963),
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16:Conjecture in number theory mathematics
154:{\displaystyle {\frac {q^{p}-1}{q-1}}}
104:{\displaystyle {\frac {p^{q}-1}{p-1}}}
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333:"Solvability of groups of odd order"
216: + 1 = 112643.
494:Unsolved problems in number theory
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208: = 3313 with common
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271:Proc. Natl. Acad. Sci. U.S.A.
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464:"Feit–Thompson Conjecture"
391:10.4310/PAMQ.2012.v8.n3.a5
171:Feit & Thompson 1963
25:Feit–Thompson conjecture
353:10.2140/pjm.1963.13.775
257:Goormaghtigh conjecture
252:Cyclotomic polynomials
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292:10.1073/pnas.48.6.968
231: = 3 (
223: = 2 (
175:Feit–Thompson theorem
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204: = 17 and
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378:Pure Appl. Math. Q.
283:1962PNAS...48..968F
461:Weisstein, Eric W.
193:was disproved by
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346:: 775–1029,
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179:finite group
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489:Conjectures
416:Math. Comp.
240:probability
177:that every
21:mathematics
483:Categories
263:References
58:such that
29:conjecture
469:MathWorld
400:1558-8599
362:0030-8730
238:Informal
197:with the
173:) of the
143:−
132:−
93:−
82:−
319:16590960
246:See also
187:solvable
111:divides
446:0297686
438:2005226
408:2900154
370:0166261
326:0143802
279:Bibcode
233:Le 2012
191:coprime
181:of odd
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210:factor
27:is a
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434:JSTOR
336:(PDF)
301:71265
297:JSTOR
183:order
167:proof
396:ISSN
358:ISSN
315:PMID
54:and
45:1962
424:doi
386:doi
348:doi
305:PMC
287:doi
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185:is
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273:,
214:pq
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382:8
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229:q
221:q
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146:1
140:q
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