A Note on Pépin's counter examples to the Hasse principle for curves of genus 1

Details A Note on Pépin's counter examples to the Hasse principle for curves of genus 1 A Note on Pépin's counter examples to the Hasse principle for curves of genus 1

1999-03-18

arxiv.org/abs/math/9903207v1

Mathematics

Number Theory

Scientific paper

In a series of articles published in the C.R. Paris more than a century ago, T. P\'epin announced a list of ``theorems'' concerning the solvability of diophantine equations of the type $ax^4 + by^4 = z^2$. In this article, we show how to prove these claims using the structure of 2-class groups of imaginary quadratic number fields. We will also look at a few related results (including FLT for $n = 7$) from a modern point of view.

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