A New Proof of Rational Cycles for Collatz-Like Functions Using a Coprime Condition
In this paper, we study the bounded trajectories of Collatz-like functions. Fix α,β∈Z>0 so that α and β are coprime. Let k¯=k1,…,kβ−1 so that for each 1≤i≤β−1, ki∈Z>0, ki is coprime to α and β, and ki≡i mod β. We define the function Cα,β,k¯:Z>0⟶Z>0 and the sequence n,Cα,β,k¯n,Cα,β,k¯2n,⋯...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2023-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2023/5159528 |
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