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Autor:
Hercher, Christian
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 numerical verification of this conjecture up to $10^7$ and $1.4\cdot 10^9$. In
Externí odkaz:
http://arxiv.org/abs/2411.01964
Autor:
Hercher, Christian, Fegert, Karl
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 complete list and a proof that these are the only numbers of this kin
Externí odkaz:
http://arxiv.org/abs/2407.21487
Autor:
Hercher, Christian, Niedermeyer, Frank
Publikováno v:
Mathematics Open 2024
Consider the set $\{1,2,\ldots,3n\}$. We are interested in the number of partitions of this set into subsets of three elements each, where the sum of two of them equals the third. We give some criteria such a partition has to fulfill, which can be us
Externí odkaz:
http://arxiv.org/abs/2307.00303
Autor:
Hercher, Christian
Publikováno v:
Journal of Integer Sequences, Vol. 26, Issue 3 (2023), Article 23.3.5
The Collatz conjecture (or ``Syracuse problem'') considers recursively-defined sequences of positive integers where $n$ is succeeded by $\tfrac{n}{2}$, if $n$ is even, or $\tfrac{3n+1}{2}$, if $n$ is odd. The conjecture states that for all starting v
Externí odkaz:
http://arxiv.org/abs/2201.00406
Autor:
Friedrich, Tobias, Hercher, Christian
Publikováno v:
In Journal of Discrete Algorithms September 2015 34:128-136
Autor:
Hercher, Christian
Publikováno v:
Überraschende Mathematische Kurzgeschichten; 2017, p85-92, 8p