7 problems

Let $(F_n^{(k)})$ be the $k$-generalized Fibonacci sequence, and let $G$ be the Galois group associated with its characteristic polynomial, viewed as a subgroup of the symmetric gr…

Conjecture on all occurrences. The solutions $(n,m)$ are exactly

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 $f_n(s,t)$ be the generalized Fibonacci sequence, and consider reciprocal sums over positive integers $n$ and $r$. The preceding theorem gives floor formulas for sums involving…

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