A132632 Minimal m > 0 such that Fibonacci(m) == 0 (mod n^2).

1, 6, 12, 12, 25, 12, 56, 48, 108, 150, 110, 12, 91, 168, 300, 192, 153, 108, 342, 300, 168, 330, 552, 48, 625, 546, 972, 168, 406, 300, 930, 768, 660, 306, 1400, 108, 703, 342, 1092, 1200, 820, 168, 1892, 660, 2700, 552, 752, 192, 2744, 3750, 612, 1092

Offset: 1

Author

Hieronymus Fischer, Aug 24 2007

Keywords

• nonn

Comments

a(n) is a divisor of the Pisano period A001175(n^2).

Examples

			a(4)=12, since Fib(12)=144==0(mod 4^2), but Fib(k) is not congruent to 0 modulo (4^2) for 1<=k<12.
		

Crossrefs

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

Programs

Mathematica

Join[{1}, Table[a = {0, 1}; k = 0; While[k++; s = Mod[Plus @@ a, n^2]; a = RotateLeft[a]; a[[2]] = s; a[[1]] != 0]; k, {n, 2, 60}]] (* T. D. Noe, Aug 08 2012 *)

Formula

a(n) = A001177(n^2)