### Math 420: Introduction to Number Theory

####
Professor Richard Kenyon

Tel. 863-6406

rkenyon -at- math dot brown dot edu

office: Kassar 305

Office hours: Mondays 2-3pm or by appointment

**Text:** J. Silverman, A Friendly Introduction to Number Theory, 4th ed.

**Course outline:**
We'll cover many of the topics of elementary number theory, including Pythagorean triples, factorization, modular arithmetic, primes, quadratic reciprocity,
and so on.
We will cover most of the material in chapters 1-30, roughly, depending on
time.

## Midterm March 14 in class

## Final May 14, 2pm, BH 155

One page of notes is allowed.

There will be homeworks collected weekly and one midterm.
The final grade will be weighted as follows:
Homework 35%, midterm 20%, final 45%.

### Homework:

Late homework will not be accepted.
The lowest homework grade will be dropped.
**Homework 1, due Tuesday Feb. 5 in class:**

1.1, 1.2, 1.3

2.1,2.5,2.8

3.2,3.4

**Homework 2, due Tuesday Feb. 12 in class:**

5.1, 5.3, 5.4,

6.1, 6.2, 6.4, 6.6,

7.3, 7.4, 7.5

**Homework 3, due Thursday Feb. 21 in class:**

8.3, 8.4, 8.6,

9.2

10.1, 10.2,

11.2, 11.7

**Homework 4, due Tuesday Feb. 26 in class:**

12.2, 12.3a,b, 12.5, 13.3, 14.1, 15.1, 15.2, 15.5

**Homework 5, due Tuesday March 5 in class:**

16.1a, 16.5, 17.2, 17.4, 18.1
(this can be done with an ordinary calculator but feel free to use a computer algebra package or wolfram alpha for help).

**Homework 6, due Tuesday March 12 in class:**

19.2, 19.3, 19.4, 19.7

**Homework 7, due Thursday March 21 in class:**

20.2a,b,c, 20.3, 21.1, 21.5, 22.6, 22.7

*No office hours March 18*

*No office hours Apr 2*

*No class Tuesday Apr 9.*

*No office hours Apr 8*

**Homework 8, due Thursday April 11 in class:**

23.5, 24.2, 24.3, 25.1, 25.5, 27.2, 27.3

Problem 25.5 solution

**Homework 9, due Tuesday April 16 in class:**

28.1, 28.4, 28.5, 29.2, 29.6

**Homework 10, due Thursday April 25 in class:**

31.1, 31.3, 31.4, 32.2, 32.4a

**Homework 11, not to be turned in; discussed in review session Tuesday April 30:**

34.1,34.2, 37.1, 37.3,37.4,37.15