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A Pythagorean Introduction to Number Theory

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Cover of 'A Pythagorean Introduction to Number Theory'

Table of Contents

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    Book Overview
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    Chapter 1 Introduction
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    Chapter 2 Basic number theory
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    Chapter 3 Integral solutions to the Pythagorean Equation
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    Chapter 4 What integers are areas of right triangles?
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    Chapter 5 What numbers are the edges of a right triangle?
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    Chapter 6 Primes of the form $$4k+1$$
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    Chapter 7 Gauss Sums, Quadratic Reciprocity, and the Jacobi Symbol
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    Chapter 8 Counting Pythagorean triples modulo an integer
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    Chapter 9 How many lattice points are there on a circle or a sphere?
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    Chapter 10 What about geometry?
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    Chapter 11 Another proof of the four squares theorem
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    Chapter 12 Quadratic forms and sums of squares
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    Chapter 13 How many Pythagorean triples are there?
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    Chapter 14 How are rational points distributed, really?
Attention for Chapter 5: What numbers are the edges of a right triangle?
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