Half an Induction Proof of the Collatz Conjecture

SummaryIn a straightforward proof by induction of the Collatz conjecture, it is easy to show that the statement is true for n=1 (the base case) but proving the induction step is more challenging—in fact, no one has done so to date. In this work, a different induction proof of the conjecture, based on a binary representation of the starting integer, is given in which it is possible to prove the induction step but there is no known proof for the base case. In fact, if one could prove the base case, then the Collatz conjecture is true. Additional informationNotes on contributorsDaniel SolowDaniel Solow (daniel.solow@case.edu) received a BS in math from Carnegie-Mellon University; an MS in Operations Research from Berkeley; and a Ph.D. in Operations Research from Stanford University. He has been a professor in the Weatherhead School of Management at Case Western Reserve University since 1978. In addition to specializing in optimization and mathematical modeling, he is best known for his seminal book titled How to Read and Do Proofs that, when published in 1982, was the first systematic approach for teaching students how to read, understand, think about and do mathematical proofs. He has also established an annual award through the Mathematical Association of America to recognize outstanding contributions of undergraduate educational materials.