Tetrated integers grow fast enough to result in fewer solutions to Diophantine equations that involve tetration. Because of this, it appears that proofs of negative results in this area may be quite elementary and easier than proofs of Diophantine equations involving exponents. For example: Tom & Ken's Last Theorem: for .
James Klein is a computer scientist and fellow traveler with Tom and Ken, fighting for "Truth, Analysis, and the Mathematical Way." Jimmy first knew about Tommy in 1959 when Tommy was in the 8th grade. It was an awkward and embarrassing encounter at the Thompson's for Jimmy who was only in the 6th grade. Jim first heard about Ken in 1966 from, at that time, Ken's future mother-in-law.
To find out what she said about Ken, and what Jimmy had to endure from the Thompsons, come to the conference in honor of Tom and Ken to hear the rest of these stories -- as well as an interesting extension of Fermat's Last Theorem to the tetration operator.