4 problems

Let $m$ be a positive integer. The Pisano period modulo $m$ is one shortest period of the Fibonacci sequence modulo $m$, and its number of zeros is the order of $m$. OEIS conjectur…

For the Fibonacci recurrence and its parity transform modulo prime powers, Self-Similarity at Prime Powers. At each transition $p^k\to p^{k+1}$, all existing periods are preserved,…

Let $p$ be prime, and let $\#(p)$ count distinct periods modulo $p$ of the Fibonacci recurrence and its parity transform over all initial conditions…

Let the Jacobsthal sequence be defined by $J_0=0$, $J_1=1$, and $J_n=J_{n-1}+2J_{n-2}$, and let $m>1$ be an integer. A modulus $m$ is a fixed point when its Pisano period equals…