A132633 Minimal m > 0 such that Fibonacci(m) == 0 (mod n^3).

1, 6, 36, 48, 125, 36, 392, 384, 972, 750, 1210, 144, 1183, 1176, 4500, 3072, 2601, 972, 6498, 6000, 3528, 3630, 12696, 1152, 15625, 7098, 26244, 2352, 11774, 4500, 28830, 24576, 21780, 5202, 49000, 3888, 26011, 6498, 42588, 48000, 33620, 3528, 81356

Offset

1,2

Comments

a(n) is a divisor of the Pisano period A001175(n^3).

Links

Table of n, a(n) for n=1..43.

Formula

a(n) = A001177(n^3)

Example

a(6)=36, since Fib(36)=14930352==0(mod 6^3), but Fib(k) is not congruent to 0 modulo (6^3) for 1<=k<36.

Mathematica

Join[{1}, Table[a = {0, 1}; k = 0; While[k++; s = Mod[Plus @@ a, n^3]; a = RotateLeft[a]; a[[2]] = s; a[[1]] != 0]; k, {n, 2, 50}]] (* T. D. Noe, Aug 08 2012 *)

Crossrefs

Cf. A000045, A001175, A001177, A130233, A130234, A131294.

Sequence in context: A328466 A232137 A008460 * A372945 A047792 A178909

Adjacent sequences: A132630 A132631 A132632 * A132634 A132635 A132636

Keyword

nonn

Author

Hieronymus Fischer, Aug 24 2007

Status

approved