{"id":{"repo_id":"ohiolink","oai_identifier":"oai:etd.ohiolink.edu:osu1366226820"},"canonical_url":"https://search.dev.ndltd.org/etd/ohiolink/oai:etd.ohiolink.edu:osu1366226820","repository":{"repo_id":"ohiolink","name":"OhioLINK","base_url":"https://etd.ohiolink.edu/acprod/odb_etd/ws/oai/oai"},"display":{"title":"Graphing Beyond Collatz","abstract":"In this thesis, we present a simple additive property found in the Collatz Graph. We also discuss the Combined Collatz Graph, as defined in [3], define the Extended Combined Collatz Graph, and discuss these graphs' relation to the Collatz Problem. We prove that all integers appear in the Super Collatz Graph which we also define in this thesis. Finally, we generalize the additive property of the Collatz Graph to the qx + r problem.","abstract_html":"In this thesis, we present a simple additive property found in the Collatz Graph. 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