Ein Satz \"{U}ber die Diophantische Gleichung $Ax^{2}-By^{4}=C$ ($C=1,2,4)$

TL;DR

This paper presents a translation and correction of Ljunggren's 1953 work on the Diophantine equation $Ax^{2}-By^{4}=C$ for specific constants, contributing to historical mathematical literature.

Contribution

It provides an English translation and correction of Ljunggren's original article on a specific class of Diophantine equations, enhancing accessibility and accuracy.

Findings

Includes original German version and English translation

Corrects Ljunggren's Satz 4

Focuses on equations with C=1,2,4

Abstract

In this document, we provide both the original German version of Ljunggren's article, "Ein Satz \"{u}ber die Diophantische Gleichung $Ax^{2}-By^{4}=C$ ($C=1,2,4$)", Tolfte Skand. Matematikerkongressen, Lund, 1953, pp.~188--194 (1954), as well as our English translation. It also contains a correction of his Satz 4.