## Spring 2005

Lectures

Section 0201:

TuTh 12:30pm-1:45pm (MTH 0403)

Section 0301:

TuTh 2:00pm-3:15pm (MTH 0303)

Instructor

Professor Niranjan Ramachandran (atma at math dot umd dot edu)

Office: Math Building 4115 (405-5080)

Office hours: Tuesdays 3:30 - 4:30pm, Wednesdays 11:00am - Noon.

Class web page

http://www.math.umd.edu/~atma/math406.html

Text

Elementary Number Theory and its applications by Kenneth H. Rosen (Fifth Edition). The book has many weblinks

and other resources. The Number Theory Web is amazing.

# Topics

The integers

Divisibility

Prime numbers

Greatest common divisor

Euclidean algorithm

Unique factorization

Congruences

Basic properties

Modular arithmetic

Euler's phi function

Fermat's, Euler's and Wilson's theorems

Chinese remainder theorem

Multiplicative Functions

Möbius inversion formula

Number and Sum of Divisors

Primitive roots

Existence of primitives roots

Index arithmetic

Legendre and Jacobi symbols

Perfect numbers, Mersenne primes

Continued Fractions

Pythagorean Triples

Fermat’s Last Theorem

Sums of squares

Pell’s equation

Gaussian Integers

Tests

There will be two 90-min tests (in class) with 125 points for each test.

No make-up tests will be given.

If you have to miss a test and you have a written excuse according to the University Policies, then you will be given 50% extra credit on the final.

The final exam (worth 150 points) will be on

Section 0201: Friday May 20th (1:30pm – 3:30pm) in MTH 0403.

Section 0301: Thursday May 19th (10:30am – 12:30pm) in MTH 0303.

Please see the webpage Final Exam for the official schedule.

Homework

Homework problems will be assigned everyday and they are due Tuesdays in class.

 Two 90-minute exams 250 points Final Exam 150 points Homework 100 points Total 500 points

Test dates (tentative)

Test 1: Tuesday, 1st of  March, in class. Update: now changed to Thursday 3/3/05.Covers Chapter 1 and Sections 3.1 through 3.5 (inclusive). No calculators.

Test 2: Tuesday, 5th of April, in class

Final exam: See above for informaton from Testudo

# Homework problems(to be updated during the semester)

Homework 1 (due 2/8/05) Solutions

Sect 1.1: 4,8,11,28,34,39,40

Sect 1.2: 3,8,15,17

Homework 2 (due 2/15/05) Solutions

Sect 1.3: 7,20,27

Sect 1.4: 4,14

Sect 1.5: 8,17,34,36,39

Homework 3 (due 2/22/05) Solutions to 3.3 and 3.4 , Solutions to others including Homework 4

Sect 3.1: 3,6,13,16

Sect 3.2: 3,10,12,16

Sect 3.3: 5,16

Homework 4 (due 3/1/05) (Solutions are above)

Sect 3.3: 21,23,32

Sect 3.4: 1,3,21

Sect 3.5: 9,11,14,15,45

Homework 5 (due 3/15/05)

Sect 4.1: 6,13,19,27

Sect 4.2: 9,13,15

Sect 4.3: 4,9,13

Homework 6 (due 3/31/05) Solutions to 4.1,4.2,4.3, 6.1, 6.3 ,

Sect 6.1: 2,16,24,28,34

Sect 6.3: 6,8,10

Homework 7 (due 4/19/05)

Sect 7.1: 6,12,16

Sect 7.2: 8,16

Sect 9.1: 6,8,14

Sect 9.2: 6,10,16

Homework 8 (due 4/26/05)

Sect 11.1: 6,10,12,14,20,28(a)

Sect 11.2: 4,6,8

Homework 9 (due 5/3/05)

Sect 13.1: 4,6,8,12,16,18

Sect 13.2: 4,6,10,20 Solutions to all problems from 7.1 onwards