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Search: id:A086797
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| A086797 |
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Discriminant of the polynomial x^n - x - 1. |
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4
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| 0, 5, -23, -283, 2869, 49781, -776887, -17600759, 370643273, 10387420489, -275311670611, -9201412118867, 293959006143997, 11414881932150269, -426781883555301359, -18884637964090410991, 808793517812627212561, 40173648337182874339601
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Selmer proved that for all n the Galois group of the polynomial x^n - x - 1 over the rationals is the symmetric group S_n. [Comment corrected by Artur Jasinski (grafix(AT)csl.pl), Feb 06 2007]
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REFERENCES
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H. Osada. The Galois groups of the polynomials X^n + a X^l + b. Journal of Number Theory, Feb. 1987, vol. 25, (no.2):230-8.
Selmer E., 1956. Mathematica Scandinavica 4, pp. 287-302.
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FORMULA
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Except for the sign, the sequence alternates between the sum and difference of consecutive terms of A000312. a(n) = (n^n + (-1)^n (n-1)^(n-1)) (-1)^Ceiling[1+n/2]. - T. D. Noe (noe(AT)sspectra.com), Aug 13 2004
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PROGRAM
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(PARI) a(n)=poldisc(x^n-x-1)
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CROSSREFS
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Cf. A000312 (n^n), A007781 (n^n - (n-1)^(n-1)), A056788 (n^n + (n-1)^(n-1)).
Cf. A086783.
Sequence in context: A156555 A116652 A072104 this_sequence A023275 A018899 A080990
Adjacent sequences: A086794 A086795 A086796 this_sequence A086798 A086799 A086800
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KEYWORD
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sign
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AUTHOR
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Yuval Dekel (dekelyuval(AT)hotmail.com), Aug 05 2003
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EXTENSIONS
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More terms from Benoit Cloitre (benoit7848c(AT)orange.fr), Aug 06 2003
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