3 papers
math.GM2020
The Mobius Function and Congruent Numbers
Roy Burson
This work provides a complete characterization of congruent numbers in terms of Pythagorean triples. Specifically, we show that every congruent number can be written as $$\frac{nm\…
math.GM2020
On the Distribution of the First Point of Coalescence for some Collatz Trajectories
Roy Burson
This paper is a numerical evaluation of some trajectories of the Collatz function. Specifically, I assess the coalescence points of each integer and $n\equiv…
math.HO2019
Integer Representations and Trajectories of the 3x+1 Problem
Roy Burson
This paper studies certain trajectories of the Collatz function. I show that if for each odd number , then every positive integer $n \in \mathbb{N}\setminus 2^{\mat…