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Elementary Number Theory and Its Applications
This latest edition of Kenneth Rosen's widely used Elementary Number Theory and Its Applications enhances the flexibility and depth of previous editions while preserving their strengths. Rosen effortlessly blends classic theory with contemporary applications. New examples, additional applications and increased cryptology coverage are also included. The book has also been accuracy-checked to ensure the quality of the content. A diverse group of exercises are presented to help develop skills. Also included are computer projects. The book contains updated and increased coverage of Cryptography and new sections on Mvbius Inversion and solving Polynomial Congruences. Historical content has also been enhanced to show the history for the modern material. For those interested in number theory.
544 pages, Hardcover
First published January 1, 1984
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425 people want to read
About the author
Kenneth H. Rosen
39 books43 followersDr. Rosen received his B.S. in Mathematics from the University of Michigan, Ann Arbor
(1972), and his Ph.D. in Mathematics from M.LT. (1976).
Dr. Rosen has published numerous articles in professional journals in the areas of number theory and mathematical modeling. He is the author of the textbooks Elementary Number Theory and Its Applications, published by Addison-Wesley and currently in its fifth edition, and Discrete Mathematics and Its Applications
(1972), and his Ph.D. in Mathematics from M.LT. (1976).
Dr. Rosen has published numerous articles in professional journals in the areas of number theory and mathematical modeling. He is the author of the textbooks Elementary Number Theory and Its Applications, published by Addison-Wesley and currently in its fifth edition, and Discrete Mathematics and Its Applications
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Displaying 1 - 7 of 7 reviews
February 17, 2016
Try working problems 12, 13, 14, 15, 16, 17, 20, 23, 25, 27, 28, 29, 33, 34, 44 and 45 of section 1.1 from the sketchy exposition provided.
Try working problems 5, 10, 14, 15, 16, 17, 21, 22, 23, and 24 from the sketchy exposition provided.in section 1.2
Try working out the proofs of Bertrand's Conjecture and Bonse's Inequality, topics which deserve their own exposition, asked for in the problems for Section 3.2.
Try understanding the least remainder theorem which deserves its own exposition, but instead is relegated to problems 14-18 of Section 3.4, much less working the problems themselves.
Problems 10-25 of Section 3.4 or over half are unworkable from the exposition!!!!!
Problems 19-42 of Section 7.5 cannot be worked from the exposition.
This is only the tip of the iceberg.
In addition numerous answers in the back of the book are completely unintelligible.
Rosen has gone out of his way to transmogrify an interesting subject into a nightmare of incomprehensibility and frustration and managed to collect royalties for it. I don't know who is more despicable, Rosen or the reviewers on this thread who are obviously lying through their teeth about this book.
In short, this book is roughly 500 pages of incomprehensible trash for which no one reading the dishonest reviews on this thread should be conned into shelling out his hard-earned dollars.
Try working problems 5, 10, 14, 15, 16, 17, 21, 22, 23, and 24 from the sketchy exposition provided.in section 1.2
Try working out the proofs of Bertrand's Conjecture and Bonse's Inequality, topics which deserve their own exposition, asked for in the problems for Section 3.2.
Try understanding the least remainder theorem which deserves its own exposition, but instead is relegated to problems 14-18 of Section 3.4, much less working the problems themselves.
Problems 10-25 of Section 3.4 or over half are unworkable from the exposition!!!!!
Problems 19-42 of Section 7.5 cannot be worked from the exposition.
This is only the tip of the iceberg.
In addition numerous answers in the back of the book are completely unintelligible.
Rosen has gone out of his way to transmogrify an interesting subject into a nightmare of incomprehensibility and frustration and managed to collect royalties for it. I don't know who is more despicable, Rosen or the reviewers on this thread who are obviously lying through their teeth about this book.
In short, this book is roughly 500 pages of incomprehensible trash for which no one reading the dishonest reviews on this thread should be conned into shelling out his hard-earned dollars.
May 24, 2024
This book has a possibility to change the way that you see the set of integers and the underlying interactions that we have made up/discovered about them. One of the most beautiful books in all of mathematics
August 8, 2025
Overall very good. I read it straight away from Swedish "gymnasium" mathematics, so for me, it was a quite technical leap in proofs and notation and formalism. I like this way of writing much better than previous material I have come across in school. What lowered my rating, however, is that in some few but not unsignificant places throughout the book, there were semantic inaccuracies in natural language; and in other places, even notational mistakes. These kind of issues might confuse the reader, as it did with me.
Example 1.27. (page 31) contains both types of problems:
"The sum of the first n Fibonnaci numbers for 3 ≤ n ≤ 8 equals 1, 2, 4, 7, 12, 20, 33, and 54."
No: there are 8 terms in the given sequence, but the given interval just allows for 6 terms. It should start at 1 ≤ n if we get that sequence.
A few lines later:
"First, we use the fact that f_n = f_(n - 1) + f_(n - 2) for n = 2, 3, ... to see that f_k = f_(k + 2) - f_(k + 1) for k = 1, 2, 3, ...."
Note the "to see that" part. The phrasing implies a logical inference between the recursions (as in f_k being derived from f_n); when rather, it is an algebraic reformulation on equivalent footing with the other recursion — not a result obtained from the recursion itself, but from the rearrangement of it. The wording suggests a hidden pattern where there is none.
Example 1.27. (page 31) contains both types of problems:
"The sum of the first n Fibonnaci numbers for 3 ≤ n ≤ 8 equals 1, 2, 4, 7, 12, 20, 33, and 54."
No: there are 8 terms in the given sequence, but the given interval just allows for 6 terms. It should start at 1 ≤ n if we get that sequence.
A few lines later:
"First, we use the fact that f_n = f_(n - 1) + f_(n - 2) for n = 2, 3, ... to see that f_k = f_(k + 2) - f_(k + 1) for k = 1, 2, 3, ...."
Note the "to see that" part. The phrasing implies a logical inference between the recursions (as in f_k being derived from f_n); when rather, it is an algebraic reformulation on equivalent footing with the other recursion — not a result obtained from the recursion itself, but from the rearrangement of it. The wording suggests a hidden pattern where there is none.
June 15, 2022
Banger Number Theory Text
February 20, 2017
Good college textbook if you study Elementary Number Theory course
Read
May 17, 2010Read chapters 1, 3, 4, 6, 7, 9, 11, 14.
January 22, 2011
This was a good introductory text we using in my undergraduate Theory of Numbers course.
Displaying 1 - 7 of 7 reviews