Donald Silberger

collaborators

3 papers

math.NT2025

On powers of the diophantine function $⋆ : x \mapsto x (x + 1)$

Donald Silberger

We treat the functions $⋆^{k} : N \to N$ where $⋆ : x \mapsto ⋆ x := x (x + 1)$ . The set ${⋆^{k} x + 1 : {x, k} \subseteq N}$ is pairwise copr…

math.NT2024

On sums of Egyptian fractions

Donald Silberger

Let $n, d$ , and $k$ be positive integers where $n$ and $d$ are coprime. Our two main results are Theorem 1. There is a partition of the infinite interval $[k d, \infty)$ of positive i…

math.CO2024

Eulerian Directed Multigraphs

Donald Silberger

For $I^$ a finite connected nontrivial directed multigraph, we prove: 1. $I^$ has a directed circuit using each directed edge exactly once if and only if both each pair of distinct…

On powers of the diophantine function ⋆:x↦x(x+1)

On sums of Egyptian fractions

Eulerian Directed Multigraphs

On powers of the diophantine function $⋆ : x \mapsto x (x + 1)$