**Meeting time:**MWF 3-4, Room 2-139**Final Exam: May 20 9:00-12:00, Room 56-154.****Text:**Niven, Montgomery, Zuckerman,*An Introduction to the Theory of Numbers.*

Instructor: David Vogan, 2-355

Office hours before final: **Thursday 5/16 3:30-4:30 p.m., Friday 5/17 3-5 p.m., Sunday May 19 3-5 p.m.**

Telephone x3-4991

Here is a syllabus and grading information: 781info2.pdf (updated 2/27 to cover April and May).

Notes on an example done in class April 17 about solving Pell's equation.

cheat sheet *INCLUDED* with
the exam Friday April 26. The present version corrects two errors
(missing factors of two in denominators) in an example for quadratic
reciprocity. (Thank you, Evan!) In the original version, the general
formulas were correct as stated, and the missing factors did not
change the powers of -1 computed; so the conclusion of the example was
correct. A third sign error in one of the main formulas (for h_i^2 -
dk_i^2) is corrected in the version of Friday morning. (Thank you,
Kelly!)

Draft of a summary of what we've done about curves. This will be added to the cheat sheet above and given to you as part of the final exam. Version B corrects a typo referring to the point at infinity (fixed a few days ago in finalCheatSheet.pdf below).

Draft of a summary of Euclidean algorithm and quadratic reciprocity to be included in the final exam cheat sheet. Version B corrects some typos in the Euclidean algorithm example. Version C adds/corrects comments about square roots modulo p.

Draft of cheat sheet to be included with final exam. It's much too long, but too bad. I welcome corrections and suggestions for additions.

**Practice problems** Some problems
not-to-hand-in about curves (meant in part as possible preparation
for the final). Here are solutions. In general I'd encourage you to understand the
solutions printed below of all the problem sets, and the solutions you
received for the two midterms.

CORRECTED pdf file for Problem Set 1 (due Monday, February 11 in class). The original had an error in 4(a), where 739 was accidentally written instead of the intended 738.

pdf file for Problem Set 1 solutions.

pdf file for Problem Set 2 (due Tuesday, February 19 in class).

pdf file for Problem Set 2 solutions.

pdf file for Problem Set 3 (due Monday, February 25 in class).

pdf file for Problem Set 3 solutions.

pdf file for Problem Set 4 (due Monday, March 4 in class).

pdf file for solutions to Problem Set 4.

pdf file for Problem Set 5 (due Monday, March 18 in class).

pdf file for solutions to Problem Set 5.

Problem set 6 is CANCELED.

pdf file for Problem Set 6 (due Monday, April 1 in class).

pdf file for solutions to Problem Set 6 .

pdf file for Problem Set 7 (due Monday, April 8 in class). Correction (mentioned in class 4/3): the last formula in Problem 2 should be proven only for j from 1 to n (not from zero to n). The file now linked here corrects that, and a small condition needed to get Q_{j} > Q_{j-1}.

pdf file for solutions to Problem Set 7.

pdf file for Problem Set 8 (due Wednesday, April 17 in class).

pdf file for solutions to Problem Set 8.

pdf file for Problem Set 9 (due Monday, April 22 in class).

pdf file for solutions to Problem Set 9.

pdf file for Problem Set 10 (due Monday, May 6 in class). This is the last assignment to hand in.