Year: 2015
Type: preprint
Abstract: In 1987, Orrin Frink introduced the concept of almost Pythagorean triples. He defined them as an ordered triple $(x,y,z)$ that satisfies the equation $x^2+y^2=z^2+1$ where $x,y$ and $z$ are positive integers. In his paper, he showed that there were infinitely many almost Pythagorean triples by giving a characterization which suggests a method on generating all of them. However, this method does not explicitly and readily give a particular almost Pythagorean triple. In this note, using basic algebraic operations, we extend his result by giving a characterization that explicitly and readily give a particular almost Pythagorean triple.
Source: arXiv (Cornell University)
Authors: Antalan, John Rafael M., Tomenes, Mark D.
Institution: Central Luzon State University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1950339331