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Search: id:A086937
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| A086937 |
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Number of distinct zeros of x^2-x-1 mod prime(n). |
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+0
7
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| 0, 0, 1, 0, 2, 0, 0, 2, 0, 2, 2, 0, 2, 0, 0, 0, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 0, 2, 0, 0, 2, 0, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 0, 0, 2, 0, 2, 2, 2, 0, 0, 2, 2, 0, 2, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 2, 0, 0, 2, 0, 2, 0, 2, 2, 2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 0, 2, 0, 2, 2, 0, 2, 2, 0, 2, 0, 0, 0, 2, 2
(list; graph; listen)
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OFFSET
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1,5
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COMMENT
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For the prime modulus 5, the polynomial can be factored as (x+2)^2, showing that x=3 is a zero of multiplicity 2. The discriminant of the polynomial is 5. Also note how this sequence is related to the Fibonacci sequence A051830; for n>3, a(n) = 2*A051830(n). - T. D. Noe (noe(AT)sspectra.com), Aug 13 2004
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LINKS
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J.-P. Serre, On a theorem of Jordan, Bull. Amer. Math. Soc., 40 (No. 4, 2003), 429-440, see p. 433.
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FORMULA
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If p = prime(n), a(n) = A080891(p) + 1.
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MATHEMATICA
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Table[p=Prime[n]; cnt=0; Do[If[Mod[x^2-x-1, p]==0, cnt++ ], {x, 0, p-1}]; cnt, {n, 105}] (from T. D. Noe)
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CROSSREFS
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Cf. A086965, A086966, A086967.
Sequence in context: A035461 A029305 A110036 this_sequence A095759 A046113 A143068
Adjacent sequences: A086934 A086935 A086936 this_sequence A086938 A086939 A086940
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Sep 23 2003
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EXTENSIONS
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Corrected and extended by T. D. Noe (noe(AT)sspectra.com), Sep 24 2003
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