MAT 311 Introduction to Number Theory, Spring 2009.
 Instructor: Olga Plamenevskaya, office 3107 Math Tower,
email: olga@math.sunysb.edu
 Office hours: Monday 12:45am1:45pm in P143, Monday 1:453:45 in 3107, or by
appointment.
 Class meetings: MWF, 10:4011:35pm, Physics 127.
References :
 I. Niven, H. Zuckerman, H. Montgomery,An Introduction to the Theory of Numbers, 5th edition.
This is the required
text; parts of the homework will be assigned from it.
Exams: there will be two midterm exams and a final exam
(TBA).
Midterm I: Monday, Mar 2, in class.
Midterm II: Monday, Apr 20, in class.
The second exam will cover the material learned since the first exam: polynomial congruences,
primitive roots and power residues, quadratic residues and reciprocity, Legendre/Jacobi symbols,
sums of squares, Pythagorean triples, and some ad hoc methods of solving equations in integers (sec. 5.4.)
Homework: weekly assignments will be posted on
this page. Homework will constitute a significant part of your course grade.
Important: Please
write up your solutions neatly, be sure to put your name on the first page and staple all pages.
Illegible homework will not be graded.
You are welcome to collaborate with others and to consult books,
but your solutions should be written up in your own words,
and all your
collaborators and sources should be listed.

Homework 1 (pdf), due Feb 4. Some solutions

Homework 2 (pdf), due Feb 11.
Some solutions

Homework 3 (pdf), due Feb 18.
Some solutions

Homework 4 (pdf), due Feb 25.
Solutions

Homework 5 (pdf), due Mar 4.

Homework 6, due Mar 18: 4,7 sec. 2.6; 3 sec. 2.7; 2, 9 sec. 2.8.
Solutions

Homework 7, due Mar 25: 8, 10, 18, 20, 22, 37 sec. 2.8.
Hint for question 37: consider two cases, n even and n odd. For n odd,
let p be the least prime divisor of n, and show that (p1,n)=1. Then think
about the order of 2 modulo p. Solutions

Homework 8, due Apr 15: 2, 9, 10 sec. 3.2; 1, 2 sec. 3.3; 8 sec. 5.3,
and one more question: find all integers that can be represented as a difference of two squares, i.e.
n=a^{2}b^{2} . This is a lot easier than sums of squares!
Solutions

Homework 9 (pdf), due Apr 29. There's a typo on
the problem sheet, I meant to assign qiestion 3 from section 7.3 not 7.2.
Solutions

Homework 10, due Mar 25: 1, 2, 3 sec. 7.4; 3, 4 sec. 7.5; 1 sec. 7.6.
Some solutions
Prerequisites: I will try to keep prerequisites to a minimum, but
some familiarity with abstract algebra and number theory will be assumed.
Syllabus: we will cover a number of topics from elementary number theory
(selected chapters of the texbook). Time permitting, the topics will include
 Divisibility, Euclidean algorithm,
 Prime numbers, Fundamental theorem of arithmetic
 Linear Diophantine equations / Congruences
 Fermat's Little Theorem, Euler's Formula
 Powers modulo m
 Public key cryptography
 Primitive roots
 Quadratic residues
 Sums of squares
 Farey fractions, rational approximation, continued fractions
 Elliptic curves
Students with Disabilities: If you have a physical,
psychological, medical, or learning disability that may impact on your
ability to carry out assigned course work, you are strongly urged to
contact the staff in the Disabled Student Services (DSS) office: Room
133 in the Humanities Building; 6326748v/TDD. The DSS office will
review your concerns and determine, with you, what accommodations are
necessary and appropriate. A written DSS recommendation should be
brought to your lecturer who will make a decision on what special
arrangements will be made. All information and documentation of
disability is confidential. Arrangements should be made early in the
semester so that your needs can be accommodated.