English

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

R2 v1 2026-06-22T11:18:29.387Z