Franz Lemmermeyer
# Pell Conics

## An Alternative Approach to Elementary Number Theory

In this book I would like to present the content of elementary
number theory using an approach based on Pell conics. The idea
is to prepare the readers for more advanced material on elliptic
curves or algebraic geometry at a very early stage. Comments
and corrections are highly welcome.
- Preface (Nov. 2012)
- Starting with the Unit Circle (Nov. 2012)
- Examples of Conics (Nov. 2012)
- Residue Class Rings (Nov. 2012)
- Pell Conics over Residue Class Rings
- Algorithmic Number Theory
- Cryptography
- Modularity (Nov. 2012)
- Hecke operators and the Herglotz trick
- L-Series
- The Rank of Pell Conics
- The Solvability of the Pell Equation
- Modular Pell varieties
- References (Nov. 2012)

The second part of this book will discuss the geometric interpretation
of the group law, Pascal's Theorem, group laws on degenerate conics
and singular cubics, Newtons' method and formal group laws, the group
law via the theory of divisors in function fields, and a few other topics.