# Generalized 3x + 1 Mappings : searching for cycles

## TL;DR

This paper investigates the existence of cycles in generalized 3x + 1 mappings, establishing conditions for their presence and developing a method to identify such cycles across various families.

## Contribution

It introduces a systematic approach to determine and find cycles in generalized 3x + 1 mappings, expanding understanding beyond the classical case.

## Key findings

- Conditions for cycle existence established
- Method for finding cycles developed
- Applicable to multiple families of mappings

## Abstract

We determine the conditions for the existence or not of cycles for several families of generalized 3x + 1 mappings and develop a method to find them.