

A345753


EulerFibonacci pseudoprimes: odd composites k such that F(k) == 5^((k1)/2) == +1 (mod k), where F(k) = A000045(k), the Fibonacci numbers.


0



146611, 252601, 399001, 512461, 556421, 852841, 1024651, 1193221, 1314631, 1857241, 1909001, 2100901, 2165801, 2603381, 2704801, 3470921, 3828001, 3942271, 4504501, 5049001, 5148001, 5481451, 6189121, 6840001, 7267051, 7519441, 7879681, 8086231, 8341201, 8719921, 9439201, 9863461
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OFFSET

1,1


COMMENTS

If p is an odd prime except 5, then F(p) == 5^((p1)/2) == +1 (mod p).
All terms found satisfy the congruence F(k) == 5^((k1)/2) == 1 (mod k). They are a proper subset of A094394.
Are there odd composites m such that F(m) == 5^((m1)/2) == 1 (mod m)? They are a proper subset (maybe empty) of A094395 (they are not in the database, below 4*10^9).


LINKS



MATHEMATICA

Select[Range[1, 10^6, 2], CompositeQ[#] && MemberQ[{1, #  1}, PowerMod[5, (#  1)/2, #]] && Divisible[5^((#  1)/2)  Fibonacci[#], #] &]


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



