C. Hercher

activity

20222025

most citedThere are no Collatz-m-Cycles with

m \leq 91

1 citations · 1 across the 7 of their papers we have counts for

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math.NT2025

On one of Erdős' Problems -- An Efficient Search for Benelux Pairs

Christian Hercher

Erdős asked for positive integers $m < n$ , such that $m$ and $n$ have the same set of prime factors, $m + 1$ and $n + 1$ have the same set of prime factors, and $m + 2$ and $n + 2$ have the…

math.NT2025

On Positive Integers $n$ with $ϕ (n) = \frac{2}{3} \cdot (n + 1)$

Christian Hercher

While solving a special case of a question of Erdős and Graham Steinerberger asks for all integers $n$ with $ϕ (n) = \frac{2}{3} \cdot (n + 1)$ . He discovered the solutions $n\in\{5, 5…

math.NT2024

On the Sum of Squarefree Integers and a Power of Two

Christian Hercher

Erdos conjectured that every odd number greater than one can be expressed as the sum of a squarefree number and a power of two. Subsequently, Odlyzko and McCranie provided numerica…

math.NT2024

Triangular Numbers With a Single Repeated Digit

Christian Hercher, Karl Fegert

The question of which triangular numbers have a decimal representation containing a single repeated digit seamed to be settled since at least the 1970s: Ballew and Weger provided a…

math.NT2022★ 1 cited

There are no Collatz-m-Cycles with $m \leq 91$

Christian Hercher

The Collatz conjecture (or ``Syracuse problem'') considers recursively-defined sequences of positive integers where $n$ is succeeded by $\frac{n}{2}$ , if $n$ is even, or $\tfrac{3…

On one of Erdős' Problems -- An Efficient Search for Benelux Pairs

On Positive Integers n with ϕ(n)=32​⋅(n+1)

On the Sum of Squarefree Integers and a Power of Two

Triangular Numbers With a Single Repeated Digit

There are no Collatz-m-Cycles with m≤91

On Positive Integers $n$ with $ϕ (n) = \frac{2}{3} \cdot (n + 1)$

There are no Collatz-m-Cycles with $m \leq 91$