Elementary Number Theory and Its Applications
Elementary Number Theory and Its Applicationsis noted for its outstanding exercise sets, including basic exercises, exercises designed to help students explore key concepts, and challenging exercises. Computational exercises and computer projects are also provided. In addition to years of use and professor feedback, the fifth edition of this text has been thoroughly checked to ensure the quality and accuracy of the mathematical content and the exercises.
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
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What Is Number Theory?
Integer Representations and Operations
Primes and Greatest Common Divisors
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