4 problems

Let $H^{(k)}$ be the $k$-generalized Fibonacci sequence with non-positive indices, and let $\mathcal{Z}(H^{(k)})=\{n\in\mathbb{Z}:H_n^{(k)}=0\}$ denote its zero set. The zero-multi…

Let $f_n(s,t)$ be the generalized Fibonacci sequence, let $\mathbb{Z}^+$ denote the positive integers, and let $\lfloor\cdot\rfloor$ be the floor function. ACMS conjecture. If…

Let $f_n(s,t)$ denote the generalized Fibonacci sequence, and let $ud$ be the $d$-adic valuation. For an integer $d'$, write $\delta{d'\mathbb{Z}}(n)=1$ if $d'$ divides $n$ and $0$…

Noe–Post conjecture. The Diophantine equation