## Essays on number theory, Volumes 1-2 |

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### Contents

Prime Numbers | 1 |

Congruence | 9 |

The Fundamental Theorem of Arithmetic | 19 |

1 other sections not shown

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### Common terms and phrases

approximation Arithmetic Functions associates coefficients common factors complete residue system complex numbers congruence congruent modulo consecutive integers consider contradiction digits division algorithm elements equation ax Euclid's Euclidean Algorithm example Exercise factorization into primes finite number form 4n formula Fundamental Theorem Gaussian integers Gaussian prime greatest common divisor Hence infinite descent infinitely many primes integers less ir(n large number mathematician MATHEMATICS STUDY GROUP Mersenne primes Method of Infinite mod 9 monic equation multiple norm notation notice number of divisors number of primes number system NUMBER THEORY odd numbers pair perfect numbers positive integers positive solutions prime divisors prime number prime triple primes less product of primes proof prove rational integers rational primes real numbers relatively prime residue class result satisfies SCHOOL MATHEMATICS STUDY sieve solution in integers solve Suppose teger Theorem of Arithmetic three divisors twin primes unique unit write