Some Diophantine Problems

Citation

Rosenthall, Edward (1944) Some Diophantine Problems. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/dchd-cd06. https://resolver.caltech.edu/CaltechTHESIS:03282025-212107174

Abstract

This thesis is concerned with the problem of exhibiting all the rational integer solutions satisfying certain diophantine equations. The thesis consists of two sections. The first section indicates how some types of diophantine equations completely reducible in a single quadratic field may he solved completely, and also the complete solution is obtained for an interesting class of cubic diophantine equations. In the past there have been many isolated investigations on the separate equations of the class considered here and at most only partial integral solutions have been given. In this thesis the complete solutions for these equations are deduced from a single multiplicative equation in a quadratic field.

In the second section Diophantine equations completely reducible in two or more different quadratic fields are considered. These equations are solved by operating on multiplicative equations in biquadratic fields.

The success of our method depends fundamentally upon the complete solution of the simple multiplicative equation xy= zw.

Thesis Files