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%I #23 Jul 30 2019 15:08:39
%S 4181,5474,5777,6479,6721,10877,12958,13201,15251,17302,27071,34561,
%T 40948,41998,44099,47519,51841,54839,64079,64681,65471,67861,68251,
%U 72831,75077,78089,88198,90061,95038,96049,97921
%N Composite n coprime to 5 such that Fibonacci(n) == Legendre(n,5) (mod n).
%C 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).
%H Amiram Eldar, <a href="/A049062/b049062.txt">Table of n, a(n) for n = 1..500</a>
%H Masataka Yorinaga, <a href="http://ousar.lib.okayama-u.ac.jp/ja/journal/mjou/19/1/article/33418">On a congruencial property of Fibonacci numbers (numerical experiments)</a>, Math. J. Okayama Univ. 19 (1976/77), no. 1, 5-10.
%H Masataka Yorinaga, <a href="http://ousar.lib.okayama-u.ac.jp/ja/journal/mjou/19/1/article/33420">On a congruencial property of Fibonacci numbers (considerations and remarks)</a>, Math. J. Okayama Univ. 19 (1976/77), no. 1, 11-17.
%t Select[ Range[ 2, 100000 ], ! PrimeQ[ # ] && Mod[ #, 5 ] != 0 && Mod[ Fibonacci[ # ] - JacobiSymbol[ #, 5 ], # ] == 0 & ]
%Y Cf. A090820.
%K nonn,nice
%O 1,1
%A _N. J. A. Sloane_
%E Yorinaga gives table up to 707000
%E More terms from _Eric Rowland_, Apr 29 2004
%E Definition corrected by _Eric Rowland_, Feb 24 2006
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