20:
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Diaz-Toca, Gema M.; Gonzalez-Vega, Laureano (2006). "On analyzing a conjecture about univariate polynomials and their roots by using Maple". In
Kotsireas, Ilias (ed.).
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Graf von
Bothmer, Hans-Christian; Labs, Oliver; Schicho, Josef; van de Woestijne, Christiaan (2007). "The Casas-Alvero conjecture for infinitely many degrees".
367:
Castryck, Wouter; Laterveer, Robert; Ounaïes, Myriam (2012). "Constraints on counterexamples to the Casas-Alvero conjecture, and a verification in degree 12".
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121:) without constant term satisfies the condition since all derivatives are zero. Another counterexample (which is separable) is
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177: ≠ 2, 3, 7, 11, 131, 193, 599, 3541, 8009. Similar results are available for degrees of the form 6
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Maple conference 2006. Proceedings of the conference, Waterloo, Ontario, Canada, July 23–26, 2006
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The conjecture is known to hold in characteristic zero for degrees of the form
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is a positive integer. Similarly, it is known for degrees of the form 3
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Dr. Casas-Alvero talking about the conjecture in a conference in the
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The conjecture is false over a field of characteristic
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has a factor in common with each of its derivatives
169: ≠ 3, 5, 7, and for degrees of the form 5
94: − 1, then the conjecture predicts that
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193: = 20 the smallest open degree.
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161: ≠ 2, for degrees of the form 4
324:Draisma, Jan; de Jong, Johan P. (2011).
185:. It has recently been established for
98:must be a power of a linear polynomial.
43:which have factors in common with their
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102:Analogue in non-zero characteristic
397:Unsolved problems in number theory
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16:Unsolved problem in number theory
326:"On the Casas-Alvero conjecture"
90: = 1, ...,
301:10.1016/j.jalgebra.2007.06.017
203:Casas-Alvero, Eduardo (2001).
1:
413:
205:"Higher order polar germs"
63:be a polynomial of degree
39:is an open problem about
189: = 12, making
37:Casas-Alvero conjecture
25:University of Barcelona
222:10.1006/jabr.2000.8727
112:inseparable polynomial
28:
333:Eur. Math. Soc. Newsl
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49:Eduardo Casas-Alvero
76:characteristic zero
254:. pp. 81–98.
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27:on March 16, 2016.
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392:Conjectures
45:derivatives
41:polynomials
33:mathematics
386:Categories
353:1292.12001
317:1127.12002
279:J. Algebra
270:1108.65046
239:0985.14012
209:J. Algebra
197:References
374:1208.5404
345:1027-488X
339:: 29–33.
252:Maplesoft
231:0021-8693
51:in 2001.
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173:where
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110:: any
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369:arXiv
360:(PDF)
329:(PDF)
305:S2CID
287:arXiv
181:and 7
69:field
341:ISSN
256:ISBN
227:ISSN
141:or 2
59:Let
349:Zbl
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