Putnam Archive — Math 115 Introduction to Number Theory

Math 115 Introduction to Number Theory4 semesters23 assignmentsNiven–Zuckerman–Montgomery, 5th ed.Prof. Kenneth A. Ribet

UC Berkeley · No stated licenseOriginal course page

Assignments are keyed to the required textbook: Niven, Ivan, Herbert S. Zuckerman, and Hugh L. Montgomery. An Introduction to the Theory of Numbers. 5th ed. Wiley, 1991. ISBN: 9780471625469. Ribet's site keeps four semesters online. Only the assignments still linked from each semester's page survive — the rest were taken down and return 404. Exam PDFs are the "questions and skeletal solutions" versions, so they carry both the problems and Ribet's worked answers.

These are a professor's personal course pages and carry no license statement. The PDFs are mirrored here for study; the canonical copies live at math.berkeley.edu.

2012Fall

Fall 2012Berkeley

The fourteen weekly assignments are listed inline on the course page rather than as PDFs. Several problems ask for computations in Sage. Section numbers refer to Niven–Zuckerman–Montgomery.

Assignments

  1. August 30, 2012
    • §1.2, problems 1, 2, 3 — all parts, using Sage
    • §1.2, problems 4b, 5, 7, 15, 25, 27, 28, 47
  2. September 6, 2012
    • §1.3, problems 2, 8, 10, 11, 13, 16, 17, 26, 28, 31
  3. September 13, 2012
    • §1.3, problems 42, 44, 48 — for 48, see the first lines of the "Basic properties" section of the Wikipedia Fermat number entry
    • §1.4, problems 3, 4
    • §2.1, problems 6, 13, 26, 30 (check using Sage), 34, 35, 36, 37, 43
  4. September 20, 2012
    • §1.2, problem 50
    • §1.3, problems 27, 29, 36
    • §1.4 — Let n = 5k + j with k ≥ 1 and j = 0, 1, 2, 3 or 4. Show that k is congruent mod 5 to the binomial coefficient "n choose 5".
    • §2.1, problems 33, 40
    • §2.2, problems 8, 9
  5. September 29, 2012
    • §2.3, problems 4, 8, 13, 14, 17, 18, 26, 27, 29, 30, 39
  6. October 4, 2012
    • §2.7, problems 1 (using Sage if possible), 6, 12
    • §2.8, problems 3, 12, 16, 18, 20, 23
  7. October 11, 2012
    • §2.8, problems 24, 25, 29, 30, 31
    • §2.9, problems 1ad, 7
    • §3.1, problems 4 (just use Sage), 5 (use Sage to compute), 6 (use Sage to avoid tedium)
  8. October 18, 2012
    • §3.1, problems 13, 14, 15, 16, 17, 18
    • §3.2, problems 6, 7, 8, 11, 13
  9. October 25, 2012
    • §2.3, problem 37
    • §2.7, problems 13, 14
    • §2.8, problems 33, 34, 35
    • §3.3, problems 14, 15
  10. November 1, 2012
    • §4.1, problems 2, 5, 9, 14, 17, 19, 34
    • §4.2, problems 10, 12, 16, 19
  11. November 8, 2012PDF
    • Given as a PDF rather than inline text.
  12. November 15, 2012
    • §10.1, problems 3, 4
    • §10.2, problems 1, 2, 4, 5, 6
    • §10.3, problem 3
    • §10.4, problem 2
  13. November 27, 2012
    • §5.4, problem 14
    • §5.6, problems 1, 9, 10 (skipping the part about "nonsingular")
    • §5.7, problems 9, 10
  14. December 6, 2012
    • §2.4, problems 16, 17, 18
    • §5.8, problem 4
    • Find the order of the point P = (94269158776925, 1102841572571055) on the elliptic curve y^2 = x^3 + 183821385707290 x + 1153449657807210 over the ring of integers modulo M = 1636998688431221. Do this by using the elliptic curve factoring method to factor M; then use Sage to compute the order of P modulo each of the factors of M.

Exams — questions with skeletal solutions

2011Fall

Fall 2011Berkeley

The best-preserved semester — five assignments plus one solution set.

Assignments

  1. Assignment 1PDF
  2. Assignment 6PDF
  3. Assignment 11PDF
  4. Assignment 12PDF
  5. Assignment 13PDF
  6. Assignment 13 solutionsPDF

Exams — questions with skeletal solutions

2006Fall

Fall 2006Berkeley

Assignments

  1. Assignment 12PDF
  2. Assignment 13PDF
  3. Assignment 14PDF

Handouts

Exams — questions with skeletal solutions

1999Fall

Fall 1999Berkeley

Exams only; no assignments remain online.

Exams — questions with skeletal solutions

Spring 1998 (math115_98.html) and Fall 2000 (math115_00.html) are still up but link to no problem sets or exams.