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Search: id:A090820
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| A090820 |
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Composite n such that Fibonacci(n) == Legendre(n,5) (mod n). |
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+0
4
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| 25, 60, 120, 125, 180, 240, 300, 360, 480, 540, 600, 625, 660, 720, 840, 900, 960, 1080, 1200, 1320, 1440, 1500, 1620, 1680, 1800, 1860, 1920, 1980, 2160, 2400, 2460, 2520, 2640, 2700, 2760, 2880, 3000, 3060, 3125, 3240, 3300, 3360, 3420
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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If n is a prime, not 5, then Fibonacci(n) == Legendre(n,5) (mod n) (see for example G. H. Hardy and E. M. Wright, Theory of Numbers).
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REFERENCES
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Yorinaga, Masataka; On a congruencial property of Fibonacci numbers-considerations and remarks. Math. J. Okayama Univ. 19 (1976/77), no. 1, 11-17.
Yorinaga, Masataka; On a congruencial property of Fibonacci numbers-numerical experiments. Math. J. Okayama Univ. 19 (1976/77), no. 1, 5-10.
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LINKS
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F. J. van de Bult, D. C. Gijswijt, J. P. Linderman, N. J. A. Sloane and A. R. Wilks, A Slow-Growing Sequence Defined by an Unusual Recurrence, J. Integer Sequences, Vol. 10 (2007), #07.1.2.
F. J. van de Bult, D. C. Gijswijt, J. P. Linderman, N. J. A. Sloane and A. R. Wilks, A Slow-Growing Sequence Defined by an Unusual Recurrence [pdf, ps].
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MATHEMATICA
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Select[ Range[ 2, 5000 ], ! PrimeQ[ # ] && Mod[ Fibonacci[ # ] - JacobiSymbol[ #, 5 ], # ] == 0 & ]
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CROSSREFS
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Cf. A049062, A093372, A094063.
Sequence in context: A125827 A163654 A063317 this_sequence A044127 A044508 A166873
Adjacent sequences: A090817 A090818 A090819 this_sequence A090821 A090822 A090823
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KEYWORD
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nonn
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AUTHOR
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Eric S Rowland (erowland(AT)math.rutgers.edu), Apr 29 2004
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