With axiom of induction , we often connect infinite descent, ie. we find and implication for mapping consecutive solutions so that we reach contradiction. In simpler crypto cases we often deal with Vieta jumping, in more advanced cases we deal with complex mapping. But now, if we are to e.g. prove that for each positive integer there exist infinitely many even positive integers which can be written in more than ways as the sum of two odd primes, then we find it troublesome to find the right mapping. Often times we could use mapping from lemmas like e.g. if is an integer, and if two coprime positive integers and are such that is a -th power of a positive integer, then both and are -th powers of positive integers. For crypto purposes we could use the basics like the fact: or that for prime there exists a prime number such that for every integer , is not divisible by , or standard things from Riemann, Gauss etc. But, the most important point I’d like to make is that the additonal intelligence used is not the descent itself, but only part of the attack on the code allowing to understand it better. Thus, I’d like to focus a bit more on the descent itself. For its use in crypto (and not only), on three things, ie. Axioms of set theory, Hilbert’s axioms and Tarski’s axioms in the context of the descent. This will be addressed in one of the later posts, and hope you will love it.
It will take me a couple of days. Please, be patient. Besides, me and my friend are in the midst of completing a new proof for of the LFT, with a new argumentation. We will try to handle the major question within a couple of months, assuming this argumentation works.
Enclosed work on blocker conjecture and function. art1
BTW, with regards to the LTF, , we have , for even , thus , thus exist such that .