## Elementary Number Theory and Its Applications
The blending of classical theory with modern applications is a hallmark feature of the text. The Fifth Edition builds on this strength with new examples and exercises, additional applications and increased cryptology coverage. The author devotes a great deal of attention to making this new edition up-to-date, incorporating new results and discoveries in number theory made in the past few years. |

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1.3.

**Mathematical**.

**Induction**. By examining the sums of the first n odd positive

integers for small values of n, we can conjecture a formula for this sum. We have

1=1, 1 + 3 = 4, 1 + 3 + 5 = 9, 1 + 3 + 5 + 7=16, 1 + 3 + 5 + 7 + 9 = 25, 1 + 3 + 5 + 7

+ ...

Use

**mathematical induction**to prove that n < 2" whenever n is a positive integer.

2. Conjecture a formula for the sum of the first n even positive integers. Prove

your result using

**mathematical induction**. 3. Use

**mathematical induction**to prove

...

Use the principle of

**mathematical induction**to show that a set of integers that

contains the integer k, such that this set contains n + 1 whenever it contains n,

contains the set of integers that are greater than or equal to k. 20. Use

mathematical ...

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### Contents

What Is Number Theory? | 1 |

Integer Representations and Operations | 43 |

Primes and Greatest Common Divisors | 67 |

Copyright | |

34 other sections not shown