The quadratic form x2−2 py2

Abstract

Using known properties of continued fractions, we give a very simple and elementary proof of the theorem of Epstein and Rédei on the impossibility in a certain case of representing −1 by the quadratic form x 2 − 2 py 2. Two of our theorems, which concern the representation of a 2 and −2 a 2, serve to extend our method to an unknown case in which −1 is not representable.