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We introduce the \emph{Collatz conjecture} and its history. Some definitionthat this conjecture has, will be expressed and with these we try to explainsome good lemma to justify the main properties of the \emph{Collatzconjecture}. With these lemmas a situation made to go through to write somemainly properties of Collatz graph on $\mathbb{Z}/10\mathbb{Z}$. Then withsomething provided it will go to draw the graph on $\mathbb{Z}/10\mathbb{Z}$.

Collatz mapping on $\mathbb{Z}/10\mathbb{Z}$