Residues of Terms of Lucas Sequences Modulo $3^k$

J. C. Saunders, R. Nicholas Stephens

The Fibonacci sequence defined by $F_0=0$, $F_1=1$, and $F_n=F_{n-1}+F_{n-2}$ has a shortest period length of $4\cdot 3^{k-1}$ modulo $3^k$ for every $k\in \mathbb{N}$. In 2011, Bun…