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Search: id:A049062
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| A049062 |
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Composite n coprime to 5 such that Fibonacci(n) == Legendre(n,5) (mod n). |
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+0
4
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| 4181, 5474, 5777, 6479, 6721, 10877, 12958, 13201, 15251, 17302, 27071, 34561, 40948, 41998, 44099, 47519, 51841, 54839, 64079, 64681, 65471, 67861, 68251, 72831, 75077, 78089, 88198, 90061, 95038, 96049, 97921
(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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MATHEMATICA
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Select[ Range[ 2, 100000 ], ! PrimeQ[ # ] && Mod[ #, 5 ] != 0 && Mod[ Fibonacci[ # ] - JacobiSymbol[ #, 5 ], # ] == 0 & ]
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CROSSREFS
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Cf. A090820.
Sequence in context: A043627 A104918 A045734 this_sequence A093372 A091982 A072322
Adjacent sequences: A049059 A049060 A049061 this_sequence A049063 A049064 A049065
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KEYWORD
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nonn,nice
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AUTHOR
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njas
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EXTENSIONS
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Yorinaga gives table up to 707000.
More terms from Eric S Rowland, Apr 29 2004
Definition corrected by Eric S Rowland, Feb 24 2006
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