Related papers: A Conjecture Equivalent to the Collatz Conjecture
We provide a proof of the Borwein Conjecture using analytic methods.
I want to show one possibility to proof the Collatz conjecture, also called 3n+1 conjecture, for any natural number N. For this, I limit my analysis on the direct odd follower of every natural odd number and show the connections between the…
A structured approach for the Collatz conjecture is presented using just the odd integers that are, in turn, divided into categories based on the roles they play such as Starter, Intermediary and Terminal. The expression 4x+1 is used as a…
Proof systems for the Relativized Propositional Calculus are defined and compared.
There is a useful counterpart of conformal prediction for e-values, called conformal e-prediction. Conformal prediction can serve as basis for testing the assumption of exchangeability, leading to conformal testing. Similarly, conformal…
We present a modification of the superposition calculus that is meant to generate explanations why a set of clauses is satisfiable. This process is related to abductive reasoning, and the explanations generated are clauses constructed over…
Kleene algebra with tests is an extension of Kleene algebra, the algebra of regular expressions, which can be used to reason about programs. We develop a coalgebraic theory of Kleene algebra with tests, along the lines of the coalgebraic…
We give an endorsement for Cornacchia's famous algorithm. Thus we do not claim anything new but an approach which is supposed to be simpler than those of previous works written with the same aim.
Collatz Conjecture is one of the most famous, for its simple form, proposed more than eighty years ago. This paper presents a full attempt to prove the affirmative answer to the question proposed by the conjecture. In the first section, we…
New cases of the multiplicity conjecture are considered.
Pomset automata are an operational model of weak bi-Kleene algebra, which describes programs that can fork an execution into parallel threads, upon completion of which execution can join to resume as a single thread. We characterize a…
The article provides a counterexample to a conjecture by Blocki-Zwonek.
We establish an analogue of the Goldbach conjecture for Laurent polynomials with positive integer coefficients.
A proof of the continuous martingale convergence theorem is provided. It relies on a classical martingale inequality and the almost sure convergence of a uniformly bounded non-negative super-martingale, after a truncation argument.
We put a new conjecture on primes from the point of view of its binary expansions and make a step towards justification.
A key component of mathematical reasoning is the ability to formulate interesting conjectures about a problem domain at hand. In this paper, we give a brief overview of a theory exploration system called QuickSpec, which is able to…
This paper presents an algorithmic method that, given a positive integer $j$, generates the $j$-th convergence stair containing all natural numbers from where the Collatz conjecture holds by exactly $j$ applications of the Collatz function.…
Timed automata and register automata are well-known models of computation over timed and data words respectively. The former has clocks that allow to test the lapse of time between two events, whilst the latter includes registers that can…
We survey recent developments on the Restriction conjecture.
A short, fairly self-contained proof is given of the Poincar\'e Conjecture. In the previous version there was an error on Page 8. This gap has now been filled.