[seqfan] Mod[Fibonacci[n],n^2]<=Mod[Fibonacci[n],n]

[zak seidov]

1.
Numbers n such that 
Mod[Fibonacci[n],n^2]<=Mod[Fibonacci[n],n]
{1,2,3,4,12,45,177,1932,2189,4712,
5771,5778,43220}
More terms?

2.
Q.Is Mod[Fibonacci[n],n^2]=0 only for n=1,12?

Thanks, Zak