## Elementary Topics in Number Theory, Algebra, and Probability |

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### Contents

Basic Operations on the Integers | 3 |

Order Axioms | 8 |

Theorems on Division | 11 |

Copyright | |

20 other sections not shown

### Common terms and phrases

52 cards addition and multiplication additive inverse algebra Appendix base cancellation law card matching problem chips worth clock arithmetic Closure Law color commutative law composite integers Compute corresponding dealt deck of 52 digits distinct primes distributive law divides Division Algorithm elevator problem equal Euclid's Algorithm example exercises exist exponents find the g.c.d. Find the probability floor form 3k greatest common divisor Hence implies integer greater jumps laws for addition least common multiple matrix modulo-five system modulo-seven system modulo-six system mosaic multiplicative inverse nonnegative integer nonzero elements number of positive number theory outcomes perfect numbers positive divisors positive integer prime factorization proof properties Prove quadratic equation quadratic formula quotients rational numbers relatively prime remainder Rn systems sample space satisfy Section 20 selecting sequence solution standard deck standard factorization student subtraction sum of multiples Suppose tables Theorem tion tosses total number uncommon primes white cards zero