Notes on the Diophantine Equation A^4+aB^4=C^4+aD^4
Number Theory
2021-07-15 v3
Abstract
A new formulation of the subject equation is presented. Several parametric and semi-parametric solutions are derived. The parametric solution for a=-1 was originally presented in 1972, but never published. A computer-generated version was found by Zajta and published in 1983. The pencil-and-paper version is presented for the record, along with many other examples, including eight coincidental triplet solutions.
Keywords
Cite
@article{arxiv.1510.03422,
title = {Notes on the Diophantine Equation A^4+aB^4=C^4+aD^4},
author = {Paul A. Roediger},
journal= {arXiv preprint arXiv:1510.03422},
year = {2021}
}
Comments
13 pages, 16 tables, previous version scrubbed thoroughly for errors