  The generalized Fibonacci sequences are sequences $\{f_n\}$ which satisfy the
recurrence $f_n(s, t) = sf_{n - 1}(s, t) + tf_{n - 2}(s, t)$ ($s, t \in
\mathbb{Z}$) with initial conditions $f_0(s, t) = 0$ and $f_1(s, t) = 1$. In a
recent paper, Amdeberhan, Chen, Moll, and Sagan considered some arithmetic
properites of the generalized Fibonacci sequence. Specifically, they considered
the behavior of analogues of the $p$-adic valuation and the Riemann zeta
function. In this paper, we resolve some conjectures which they raised relating
to these topics. We also consider the rank modulo $n$ in more depth and find an
interpretation of the rank in terms of the order of an element in the
multiplicative group of a finite field when $n$ is an odd prime. Finally, we
study the distribution of the rank over different values of $s$ when $t = -1$
and suggest directions for further study involving the rank modulo prime powers
of generalized Fibonacci sequences.
