Regular office hours
Tu 11noon,
Th 121,
Fri 23
Office telephone: 642 0648
Fax number: 642 8204
Secretary: 642 5026
Exam week office hours:
 Monday, December 11  23:30PM
 Tuesday, December 12  11:30AM12:30PM
email:
ribet@math.berkeley.edu
Textbook
Elementary
Number Theory and its applications
by Kenneth H. Rosen.
You want the fourth edition. The publisher is Addison Wesley Longman.
This book lists for $86 but can be had cheaper online.
One place to shop is
evenbetter.com, which claims
a price of $46.03 airshipped from a company in England!
As you can infer from
the publisher's
web
page for our book, a companion
website has been created.
When I taught this course last year,
I used
An
Introduction to the Theory of Numbers
by Ivan Niven, Herbert S. Zuckerman and Hugh L. Montgomery
as a text.
For alternative possibilities, check out
my guide to
recent and classic books
on number theory.
When you discover misprints in the textbook, please
email me with what
you've found. I'm compiling a list, which I'll send to the author
at the end of the semester.
Syllabus
According to the
General
Catalog,
this course treats
``Divisibility, congruences, numerical functions, theory of primes.
Topics selected: Diophantine analysis, continued fractions,
partitions, quadratic fields, asymptotic distributions, additive problems.''
It has been my intention to emphasize applications to cryptography in
this course. Our textbook was recommended by a mathematician at another
university who taught a course like this from a similar perspective.
It looks as if I will follow the book's table of contents, treating
Chapters 1 and 2 pretty superficially. We should certainly be able
to cover Chapter 8, which treats cryptology. By the end of the course,
we should have covered the very important Chapter 11. If there's time,
we'll talk about continued fractions as well (Chapter 12).
Examinations
 First Midterm: Friday, September 29
(questions and answers).
Here's how the scores were distributed:
Median = 20
Average = 19.2
Maximum possible score = 30
 Second Midterm, Friday, November 3
(questions and answers).
Here's how the scores were distributed:
Median = 18
Average = 18.6
Maximum possible score = 30
 Final Exam, Wednesday December 13, 12:303:30 (exam group #2),
141 McCone Hall
(questions and answers).
Here's how the scores were distributed:
Median = 30
Average = 29.7
Maximum possible score = 50
The exams are closedbook examinations. No
calculators are allowed. On the other hand, arithmetic answers do not
have to be simplified for full credit.
Please bring your own blue books to the exams.
If you'd like to see some questions that I've given in exams for this
course before, you can look at the
Spring, 1998
and the
Fall, 1999 questions.
The first of these courses was taught in 50minute MWF courses, while
the second was taught in 80minute TuTh courses.
These documents, by the way, are in
Adobe
Acrobat format.
Homework
Homework will be assigned weekly. The grader for this course
is John Voight.
The assignment
will be discussed in class on the day that it is due.
Therefore,
late homework cannot be accepted!
For numerical problems,
the grader encourages you to use computer software as you see
fit. Be sure, however, to include printouts that explain what
you did.
Your homework score for the class is computed in such a way
that your lowest score is ignored and your next lowest score
is given only half its usual weight. There will be 14 assignments,
each worth 20 points. Thus the maximum possible homework score
will be 250.

Assignment due September 6:
 § 1.4:
5cd, 6, 8, 14, 17, 30, 36
 § 3.1:
5, 7, 10, 16, 25

Assignment due September 11:
 § 3.2: 9, 15, 16, 25
 § 3.3: 1a, 3a, 5c, 7c, 9
 § 3.4: 3, 7

Assignment due September 18:
 Write the product (xa)(xb)(xc)...(xz) a simply as possible.
 Check out the
schedule
for the
MSRI Chern
conference
that begins on September 14.
The talks on September 16 are intended for a very wide audience.
By the way, you might be interested in other
MSRI activities this semester.
See for example
the number theoretic cryptographgy workshop and the
associated short course on complexity.
 § 3.4: 10, 14, 15, 17, 18
 § 3.5: 3ac, 4a
 § 3.6: 2ace
 § 4.1: 3, 6def, 7, 16, 28

Assignment due September 25:
 § 4.2: 2ab, 4 (assume that m is prime!), 6, 8d, 12, 16
 § 4.3: 4c, 8, 22
 § 4.4: 2abc, 9, 10

Assignment due October 4:
 § 4.5: 2ab, 7, 8bc
 § 4.6: 1f
 § 5.1: 4, 12, 22

Assignment due October 11
 § 6.1: 4, 6, 10, 12, 14, 16, 26, 28
 § 6.2: 6
 Browse the companion
website for our textbook. It has just been put on line.
 Look at the Prime Pages,
which are maintained by
Chris Caldwell, a number
theorist who got his doctorate
from Berkeley.
The Mersenne
prime page mentions the conjecture that there are infinitely
many Mersenne primes and infinitely many composite numbers of the
form 2^{p}1 with p prime.

Long and hard assignment due October 16:
 § 6.3: 2, 6, 10, 18
 § 7.1: 6, 10, 14, 22
 § 7.2: 2def, 4, 10, 12
 § 7.3: 4ac, 6, 10, 16

Assignment due October 23:
(Note that the
numbertheoretic cryptography workshop begins
at the MSRI on October 16.)
 § 7.4: 11, 12, 23, 24
 § 9.1: 2cd, 4def, 10, 12, 18
 § 9.2: 2cd, 6, 8, 11, 12, 16 (for this one, take p>5)
Our grader,
John Voight,
will be lecturing on
perfect
numbers in class on Friday, October 27.

Assignment due October 30:
 § 9.3: 6ad, 8ad, 10, 14, 15, 16
 § 9.4: 2ab, 4, 8, 9, 10

Assignment due November 8:
 § 9.5: 2, 4, 5, 8
 § 8.1: 4, 6, 8, 10
 § 8.2: 2, 8, 10ab

Assignment due November 15:
 § 8.4: 2, 6
 § 11.1: 5, 6, 7, 10, 12, 14, 27
 § 11.2: 4, 6
Note that office hours on November 16 will be 23PM instead of 121PM.

Assignment due November 22:
 § 11.2: 10, 11, 12 [Note that much of #12 will be done in class
on November 15.]
 § 11.3: 1cd, 5, 6
 Suppose that p is an odd prime and that p is the sum of asquared and
bsquared. If a is odd, show that a is a square modulo p.
Example: the prime 977 is the sum of the squares of 31 and 4; we may
conclude that 31 is a square modulo 977.

Assignment due December 1:

Assignment due December 8:
 § 12.1: 9f, 13
 § 12.2: 2ef, 4ae, 8
 § 12.3: 1ac, 2ab, 5
 § 12.4: 6ac
Grading
The final course grade will be computed by weighting the exams and
homework roughly as follows: midterm exams, 15% each; homework, 20%;
final exam, 50%. I reserve the right to change the mix at the
end of the semesterone can often see only after the fact how
successful a given exam has been.
I last taught this course two semesters ago. The final
grade distribution in the class was as follows (I neglect +'s and 's):
15 A's, 13 B's, 4 C's, and 2 D's.
Grades were lower than this when I taught the course five semesters ago.
Miscellaneous links related to number theory and/or this course
The campus maintains an
official
Web page
for this course, but it's only a skeleton page.
Kenneth A. Ribet
,
Math Department 3840, Berkeley CA 947203840
This page last modified