arXiv subjects

Christian Wolird

Publications and source records attributed to Christian Wolird.

2 recordsLinked to original sources

arXiv2025

The Forestry of Adversarial Totient Iterations

We give a closed-form expression for $\varphi(1+\varphi(2+\varphi(3+...+\varphi(n)$, where $\varphi$ is Euler's totient function. More generally, for an integer sequence $A=\{a_j\}$ we study the value of $A^\varphi(n)=\varphi(a_1+\varphi(a_2+\varphi(a_3+...+\varphi(a_n)$ when $A$ is the perfect squares or the perfect cubes. We show $A^\varphi(n)$ is bounded for all sequences considered. We also present the Arboreal Algorithm which can sometimes determine a closed form of $A^\varphi(n)$ using tree-like structures.

math.NT↗

arXiv2023

A New Transformation of the Magic Square of Squares

We show arithmetic triplets of Gaussian squares are in 3-to-1 correspondence with Pythagorean triples thereof. This correspondence would transform a solution to the Magic Square of Squares puzzle into a larger structure of perfect Gaussian squares. In particular, we obtain the backwards result that a puzzle solution would generate non-trivial near-miss solutions in the Gaussian integers. Results are applied to popular near-misses.

math.HO↗