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Can anyone please suggest a book or a link to website where I can find Practice questions (and there solutions) on Number Theory. More specifically questions on the following topics:

  1. Divisibility
  2. Greatest Common Denominator
  3. Congruences
  4. Fermat's Little Theorem
  5. The RSA crptosystem
  6. El Gamal cryptosystem
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google.co.in/… –  lab bhattacharjee Dec 1 '12 at 18:23

2 Answers 2

If you're looking for challenging exercises:

For practice in mastering some of the concepts needed in elementary number theory,

  • see the Kahn Academy for videos and exercises related to divisibility, gcd, congruences, etc. Under "applied math" there you can also explore cryptography problems.
  • Abstract Algebra Study Guide Chapter 1: integers: divisors/divisibility, primes, congruences, integers modulo n; Chapter 2: equivalence relations, permutations. Both chapters have both problems and solutions.
  • 250 problems in number theory has both problems and solutions.
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I love my AAA - usually "good sports"...I'll cross my fingers that you won't need to head out to get them! –  amWhy May 11 '13 at 2:10
Oh well, I'll see you soon (if not tonight, tomorrow!) –  amWhy May 11 '13 at 2:15
Nice list of challenging exercises! –  Sami Ben Romdhane Apr 17 at 15:48

I would categorize all of the books below as applied. There are many wonderful books on theoretical number theory and cryptography also and those can be added too - those were left off as you were looking for more applied books. None are in any specific order.

You also may want to visit your college library and see other examples. Lastly, you may want to search out books that are posted online (legal ones of course) and open course-ware in these areas (like MIT, Berkeley and many others).

Elementary Number Theory Related Books

  1. Elementary Number Theory [Hardcover] David Burton (Author)

  2. Elementary Number Theory: Second Edition (Dover Books on Mathematics) [Paperback] Underwood Dudley (Author)

  3. Elementary Theory of Numbers (Dover Books on Mathematics) [Paperback] William J. LeVeque (Author)

  4. Number Theory (Dover Books on Mathematics) [Paperback] George E. Andrews (Author)

  5. An Introduction to the Theory of Numbers [Paperback] G. H. Hardy (Author), Edward M. Wright (Author), Andrew Wiles (Author), Roger Heath-Brown (Editor), Joseph Silverman (Editor)

  6. Elementary Number Theory (Springer Undergraduate Mathematics Series) [Paperback] Gareth A. Jones (Author), Josephine M. Jones (Author)

  7. Number Theory and Its History (Dover Books on Mathematics) [Paperback] Oystein Ore (Author), Mathematics (Author)

  8. Friendly Introduction to Number Theory, A (3rd Edition) by Joseph H. Silverman (Mar 31, 2005)

  9. Elementary Number Theory (6th Edition) by Kenneth H. Rosen (Apr 9, 2010)

  10. Basic Number Theory (Classics in Mathematics) by André Weil (Feb 15, 1995)

  11. Excursions in Number Theory (Dover books explaining science) by C. Stanley Ogilvy (Nov 1, 1988)

  12. An Adventurer's Guide to Number Theory by Richard Friedberg (Jan 9, 1995)

  13. A Course in Number Theory and Cryptography (Graduate Texts in Mathematics) [Hardcover] Neal Koblitz (Author)

  14. Number Theory for Computing by Song Y. Yan and M.E. Hellmann (Dec 10, 2010)

  15. Elements of Number Theory (Undergraduate Texts in Mathematics) [Paperback] John Stillwell (Author)

  16. Number Theory: A Lively Introduction with Proofs, Applications, and Stories [Hardcover] James Pommersheim (Author), Tim Marks (Author), Erica Flapan (Author)

  17. Computational Intro. to Number Theory... (2ND 09) Shoup (Hardback | ISBN10: 0521516447; ISBN13: 9780521516440)

  18. Elementary Number Theory with Applications, Second Edition [Hardcover] Thomas Koshy (Author)

  19. Elementary Number Theory in Nine Chapters [Paperback] James J. Tattersall (Author)

  20. Elementary Number Theory, Cryptography and Codes (Universitext) [Paperback] M. Welleda Baldoni (Author), Ciro Ciliberto (Author), G.M. Piacentini Cattaneo (Author), Daniele Gewurz (Translator)

Cryptography Related Books

  1. An Introduction to Mathematical Cryptography (Undergraduate Texts in Mathematics) [Hardcover] Jeffrey Hoffstein (Author), Jill Pipher (Author), J.H. Silverman (Author)

  2. Cryptanalysis of Number Theoretic Ciphers (Computational Mathematics) by Samuel S. Wagstaff (Dec 10, 2002)

  3. Cryptological Mathematics (Mathematical Association of America Textbooks) [Paperback] Robert Edward Lewand (Author)

  4. The Mathematics of Ciphers: Number Theory and RSA Cryptography by S. C. Coutinho

  5. An Introduction to Cryptography (Discrete Mathematics and Its Applications) by Richard A. Mollin

  6. Lawrence C. Washington – Elliptic Curves: Number Theory and Cryptography ISBN 1-58488-365-0

  7. A. J. Menezes, P. C. van Oorschot, and S. A. Vanstone – Handbook of Applied Cryptography ISBN 0-8493-8523-7

  8. Understanding Cryptography: A Textbook for Students and Practitioners [Hardcover] Christof Paar (Author), Jan Pelzl (Author), Bart Preneel (Foreword)

  9. An Introduction to Mathematical Cryptography (Undergraduate Texts in Mathematics) [Hardcover] Jeffrey Hoffstein (Author), Jill Pipher (Author), J.H. Silverman (Author)

  10. Cryptanalysis: A Study of Ciphers and Their Solution [Paperback] Helen F. Gaines (Author)

  11. Understanding Cryptography: A Textbook for Students and Practitioners [Hardcover] Christof Paar (Author), Jan Pelzl (Author), Bart Preneel (Foreword)

  12. Applied Cryptography Second Edition Bruce Schneier

  13. Guide to Elliptic Curve Cryptography, Darrel Hankerson, Alfred J. Menezes, Scott Vanstone

Try the following problem sets:

  1. http://www.math.muni.cz/~bulik/vyuka/pen-20070711.pdf

  2. http://f2.org/maths/250probs/

  3. http://www.staff.science.uu.nl/~beuke106/getaltheorie/pen0795.pdf

  4. http://www.mai.liu.se/~pehac/kurser/TATM54/booktot.pdf

Web Sites

  1. http://en.wikibooks.org/wiki/Cryptography

Enyoy! `Amzoti

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Yes, please that would be very helpful –  Farrukh12 Dec 2 '12 at 11:51
+1 I remember this thread! ;-) –  amWhy May 12 '13 at 0:20
@amWhy: that is a pretty nice list! Thanks –  Amzoti May 12 '13 at 0:44

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