## A friendly introduction to number theoryStarting with nothing more than basic high school algebra, this volume leads readers gradually from basic algebra to the point of actively performing mathematical research while getting a glimpse of current mathematical frontiers.Features an informal writing style and includes many numerical examples. Emphasizes the methods used for proving theorems rather than specific results. Includes a new chapter on big-Oh notation and how it is used to describe the growth rate of number theoretic functions and to describe the complexity of algorithms. Provides a new chapter that introduces the theory of continued fractions. Includes a new chapter on Continued Fractions, Square Roots and Pell's Equation. Contains additional historical material, including material on Pell's equation and the Chinese Remainder Theorem.A useful reference for mathematics teachers. |

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### Contents

Introduction | 1 |

What Is Number Theory? | 6 |

Pythagorean Triples | 13 |

Copyright | |

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### Common terms and phrases

approximately binomial coefficient Carmichael number Chapter complex numbers composite number compute conjecture continued fraction convergents described digits Diophantine divides divisible ee 1 mod elliptic curve ep(a equal Equation Theorem Euclidean algorithm Euler's Euler's phi function exactly example Exercises exponent fact Fermat's Little Theorem Fibonacci number Fibonacci sequence Gaussian integers Gaussian primes gcd(a gives guess Hint infinitely many primes Legendre symbol look mathematical Mersenne primes method modp modulo 13 multiple nonresidue nonzero number theory ordinary integers p-defects pattern Pell's equation perfect numbers Pigeonhole points polynomial positive integers prime number primitive Pythagorean triple primitive root modulo product of primes proof prove Pythagorean triples Quadratic Reciprocity quadratic residue quadratic residue modulo Rabin-Miller rational coordinates relatively prime remainder satisfy smallest solution solve successive squaring Suppose triangular number true values verify Write a program