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A090820 Composite n such that Fibonacci(n) == Legendre(n,5) (mod n). 4
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, 3600, 3660, 3720 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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).

LINKS

Table of n, a(n) for n=1..46.

Masataka Yorinaga, On a congruencial property of Fibonacci numbers (numerical experiments), Math. J. Okayama Univ. 19 (1976/77), no. 1, 5-10.

Masataka Yorinaga, On a congruencial property of Fibonacci numbers (considerations and remarks), Math. J. Okayama Univ. 19 (1976/77), no. 1, 11-17.

MATHEMATICA

Select[ Range[ 2, 5000 ], ! PrimeQ[ # ] && Mod[ Fibonacci[ # ] - JacobiSymbol[ #, 5 ], # ] == 0 & ]

PROG

N=10^9; for(n=2, N, if(Mod((fibonacci(n)), n)==kronecker(n, 5) && !isprime(n), print1(n, ", ")));

CROSSREFS

Cf. A049062, A093372, A094063.

Sequence in context: A163654 A063317 A241505 * A044127 A044508 A166873

Adjacent sequences:  A090817 A090818 A090819 * A090821 A090822 A090823

KEYWORD

nonn

AUTHOR

Eric Rowland, Apr 29 2004

EXTENSIONS

More terms from Felix Fröhlich, Apr 24 2014

STATUS

approved

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Last modified March 24 01:20 EDT 2019. Contains 321444 sequences. (Running on oeis4.)