Donald Silberger

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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.NT2024

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…

On sums of Egyptian fractions

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

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