## A Friendly Introduction to Number TheoryFor courses in Elementary Number Theory for non-math majors, Mathematics/Number Theory for mathematics education students, Number Theory and Computer Science. This is an introductory undergraduate text designed to entice non-math majors into learning some mathematics, while teaching them to think mathematically at the same time. Starting with nothing more than basic high school algebra, the reader is gradually led from basic algebra to the point of actively performing mathematical research while getting a glimpse of current mathematical frontiers. The writing style is informal and includes many numerical examples, which are analyzed for patterns and used to make conjectures. The emphasis is on the methods used for proving theorems rather than on specific results. *NEW - New chapter on Number Theory and Imaginary Numbers, Gaussian Integers and Unique Factorization, Irrational Numbers and Transcendental Numbers, Fibonaccis Rabbits and Linear Recurrence Sequences, Generating Functions, Sums of Powers, Binomial Coefficients and Pascal's Triangle, Primality Testing and Carmichael Numbers. *Low key introduction to Number Theory. Allows students to explore an area of maths different from |

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### Contents

Introduction | 1 |

Chapter 1 What Is Number Theory? | 7 |

Pythagorean Triples | 13 |

Copyright | |

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### Common terms and phrases

algebraic number answer binomial coefficient Carmichael number complex numbers composite numbers compute congruent conjecture cp cp cp digits Diophantine divides divisible elliptic curve ep(a equal equation x2 Euclidean algorithm Euler's phi function exactly example Exercises for Chapter exponent fact Fermat's Little Theorem Fibonacci number Fibonacci sequence formula Gaussian integers Gaussian primes gcd(a gives greatest common divisor infinitely many primes Legendre symbol look mathematical Mersenne primes method Modularity modulo 13 multiple nonresidue nonzero number theory ordinary integers p-defects pattern Pell's equation perfect numbers Pigeonhole pigeons 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 satisfying solve square-triangular number Squares Theorem successive squaring suppose triangle true values verify