The Collatz conjecture has been a famous unsolved problem in mathematics for almost a century. This proof is a complete formal proof that can be verified by anyone in the theorem proving support system Coq.
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Kobayashi, Teruyuki; Kobayashi, Yoko (2023). The formal proof of 3x+1 problem. figshare. Collection. https://doi.org/10.6084/m9.figshare.c.6472138.v1