Math 25
Number Theory
Last updated May 31, 2008 12:24:21 EDT

General Information Syllabus HW Assignments


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Homework Assigments

Week of September 20 - 24, 2004
All problems assigned this week are due on Wednesday, 9/29.
Solutions to this assignment are available here.
Assignments Made on:
Monday:
  • Study: No class
  • Do: Whatever you see fit...
Wednesday:
  • Study: Sections 1.2 and 1.4
  • Do: pp 22 - 23: 3, 15, 24
    pp 34 - 35: 6, 8, 17
Friday:
  • Study: Section 3.1
  • Do: pp 76 - 78: 2, 11, 13, 21, 24, 29
    Plus: Show that for any real number x the quantity [2x]- 2[x] is either 0 or 1.


Week of September 27 - October 1, 2004
(Due Wednesday, October 6)
Solutions to this assignment are available here.
Assignments Made on:
Monday:
  • Study:Section 3.2
  • Do: pp 84 - 85: 5, 8, 9, 20, 22, 31
Wednesday:
  • Study:Sections 3.3, 3.4
  • Do: pp 104 - 109: 8, 13, 16 (only the base 10 part), 34, 43 (part b does not need part a), 69
Friday:
  • Study: Sections 3.5, 3.6, 13.1 (only through Lemma 13.3)
  • Do: pp 117 - 119: 4 (you may assume all the numbers given are prime or products of two primes), 24
    pp 123 - 125: 2, 4, 13
    p 486: 2


Week of October 4 - 8, 2004
(Due Wednesday, October 13)
Solutions to this assignment are available here.
Assignments Made on:
Monday:
  • Study: Sections 13.1, 13.2, and the beginning of 4.1
  • Do: pp 486 - 487: 5, 12
    pp 494 - 495: 4 (just give it a shot; it might be rather hard), 10
    pp 135 - 138: 3, 8, 10, 17
Wednesday:
  • Study: Section 4.1
  • Do: pp 135 - 138: 3, 5, 7, 8, 17, 28c
Friday:
  • Study: Section 4.2
  • Do: pp 135 - 138: 16, 22
    pp 141 - 143: 2, 6, 16, 18
    pp 149 - 151: 14 (Since we don't know CRT yet, solve this using Dirichlet's theorem on primes in progressions.


Week of October 11 - 15, 2004
(Due Wednesday, October 20)
Solutions to this assignment are available here.
Assignments Made on:
Monday:
  • Study: Sections 4.2 and 4.3
  • Do: pp 141 - 143: 8,10
    pp 149 - 152: 10, 12, 18, 22, 34
Wednesday:
  • Study: Section 4.4
  • Do: pp 149 - 152: 14 (do this problem again, but using CRT this time), 30
    pp 158 - 159: 2, 8
Friday:
  • Study: Section 4.4
  • Do: pp 158 - 159: 6
    Plus: These additional problems.


Week of October 18 - 22, 2004
(Due Wednesday, October 27)
Assignments Made on:
Monday:
  • Study: Sections 5.1 and 5.2
  • Do: pp 34 - 37: 31. Show also that the result of this exercise implies that [C/4 + Y/400] = [C/4] (notation from lecture; see also p 181).
    pp 177 - 179: 2, 4, 17, 19, 22
Wednesday:
  • Study: Section 5.5
  • Do: p 183: 3, 7
    pp 194 - 196: 2, 6, 12, 14, 20 (optional)
Friday:
  • Study: Section 6.1
  • Do: pp 202 - 204: 4, 16, 20, 24
    Plus: These problems on the formula for the nth prime number


Week of October 25 - 29, 2004
(Due Wednesday, November 3)
Assignments Made on:
Monday:
  • Study: Sections 4.6 and 6.1
  • Do: p 172: 1e, 1f
    pp 202 - 204: 26, 27, 28, 32, 34 (part (a) of this problem is *false* as stated. The hypothesis should be (-1)^r * r! congruent to 1 mod p. The conclusion is wrong, too. What should the conclusion actually be?)
Wednesday:
  • Study: Section 6.2
  • Do: pp 213 - 214: 2, 8, 16, 18, 20
Friday:
  • Study: Section 6.3
  • Do: pp 213 - 214: 13, 14
    pp 218 - 219: 4, 6, 10, 12


Week of November 1 - 5, 2004
(Due Wednesday, November 10)
Assignments Made on:
Monday:
  • Study: Sections 8.1, 8.2
  • Do: pp 267: 6, 10, 12, 16
    pp 278 - 281: 2, 6, 14
Wednesday:
  • Study: Section 8.2
  • Do: Something fun. No homework assigned today.
Friday:
  • Study: Notes
  • Do: These problems on linear systems of congruences and cryptanalysis.
    You will need to use Maple (the software, not the syrup) to do these problems. Dartmouth students can download it for free here.
    You will also need this Maple file of Cryptographic tools. To use it, open it and press enter repeatedly until you get to a blank command prompt. (Slightly) more detailed instructions are available here.
    Troubleshooting: If you have trouble using the Maple file, make sure its name ends with ".mw". Some web browsers change the extension to ".xml" when the file is downloaded. If this doesn't help, try downloading this text file containing all the Maple code. To use it, copy each block of code into Maple, pressing enter after each block.
    If you have any other problems using Maple, let me know ASAP.


Week of November 8 - 12, 2004
(Due Wednesday, November 17)
Assignments Made on:
Monday:
  • Study: Section 8.2
  • Do: pp 278 - 281: 8, 28 (you should use the Maple procedures available above for these), 10, 16
Wednesday:
  • Study: Sections 8.3 and 8.4
  • Do: p 284: 4,6
    pp 290 - 291: 2, 8
    Plus: These additional problems.
Friday:
  • Study: The Beginning of Section 7.1
  • Do: pp 227 - 231: 40, 42, 44 Also: Prove the converse of Exercise 44: If f(1) = 1 and f has the factorization property of the exercise, then f is completely multiplicative.


Week of November 15 - 19, 2003
(Due Monday, November 29)
Assignments Made on:
Monday:
  • Study: The rest of Section 7.1, Section 7.2
  • Do: pp 227 - 231: 6, 8, 16, 28, 30
Wednesday:
  • Study: Notes, Sections 7.2 and 7.4
  • Do: pp 235 - 236: 4, 12
    pp 256 - 257: 10, 17, 18, 20, 26 (use the method of Euler products introduced in class for 18, 20 and 26),
Friday:
  • Study: Notes, beginning of Section 2.3
  • Do: These problems on square-free integers.


Week of November 22 - 26, 2004
(Due Wednesday, December 1)
Assignments Made on:
Monday:
  • Study: Section 11.1
  • Do: pp 386 - 390: 4, 6, 8, 10 (the last Legendre symbol should be computed at (p-1)b, not (p-1)/b), 50


Week of November 29 - December 3, 2004
(Due Saturday, December 4)
Assignments Made on:
Monday:
  • Study: Section 11.2
  • Do: Work on the Final Exam
Wednesday:
  • Study: Notes
  • Do: Work on the Final Exam


Ryan Daileda
Last updated May 31, 2008 12:24:21 EDT