A090820 Composite n such that Fibonacci(n) == Legendre(n,5) (mod n).

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

Offset: 1

Author

Eric Rowland, Apr 29 2004

Keywords

• nonn

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

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• 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.

Crossrefs

Cf. A049062, A093372, A094063.

Programs

Mathematica

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

PARI

N=10^4; for(n=2,N, if(Mod((fibonacci(n)), n)==kronecker(n,5) && !isprime(n), print1(n, ", ")));

Extensions

More terms from Felix Fröhlich, Apr 24 2014