# JHR's MA378 page

## MA378

Number Theory

MTRF 9, G308

John Rickert,
Associate Professor of Mathematics

**Office:** G-215A, Crapo Hall

**Phone:** (812) 877-8473

**CM**: 141

**e-mail:** john.rickert@rose-hulman.edu

Schedule

To Homework
...Questions
...random notes
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Homework for our next class
...Today's questions
...Today's notes
... sequences

The main goal in this class is to have you (the student) perform as an active learner. To do this you will need to do the exercises, raise questions about structures that you are studying, create hypotheses and test these hypotheses.

The textbook for this class is *An Introduction to the Theory of Numbers*, 5th Ed., by Niven, Zuckerman and Montgomery.

#### Homework

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For *Tuesday, March 8*: Work on exercises Section 1.2 #5,11,23. (Note that pattern in this sequence of numbers!)

For *Thursday, March 10*:
Work on exercises Section 1.2 # 1,3,31.

For *Friday, March 10*:
Let *a*_{n} be the smallest positive integer so that there is a positive integer *b*_{n} for which the Euclidean algorithm requires at least *n* steps to find the GCD of *a*_{n} and *b*_{n}.

A copy of the *Maple* file used in class is available on ANGEL.

For *Monday, March 14*:
Turn in the six exercises from Section 1.2.

Start working on the problems
Section 1.3 #1,3,4,9,11,16,26,30,31,32,33,48.
Turn in these exercises on Friday March 25.

For *Thursday, March 17*
Section 1.3 #1,3,4,9,11,16,26,30,31,32,33,48.
Turn in these exercises on Friday March 25.<

For *Friday, March 18*:
Section1.4 #1,3,7.

For *Monday, March 21*:
We showed in class that if *n* is prime then
2^{n} == 2 (mod *n*).
Can you prove that

If 2^{n} == 2 (mod *n*) then *n* is prime?

For *Thursday, March 24*:
Section 2.1 #1,5,9,13.

For *Friday, March 25*:
Turn in the Section 1.3 and 1.4 exercises.

Section 2.1 #6,11,14,19,20;

For *Monday, March 28*:
Section 2.1 #23, 27,28*,30*,44,45. (for 28 and 30 replace the exponent `400` with `4*10`^{400}.)

*Friday, April 1*:
bring a computing device of some sort. We will work on an worksheet.

For *Monday, April 4*:
Turn in your work for the automorphic numbers worksheet.
A copy of the worksheet is available on ANGEL.

Upcoming exercises:

Section 2.2 #4,5,14.

Section 2.3 #9,14,37.

*Friday, April 8*: Exam #1

Section 2.4 #4,14,15.

Section 2.6 #9.
Turn in homework through Section 2.6 on Tuesday, April 26.

Section 2.7 #2,4,6,12.

Section 2.8 #6,10,19,23. (We have not dicussed all of sction 2.8 as of break)

Section 2.9 #1,4.

section 2.10 #1,4,7.

Section 2.11 #1,6,15,16,22.

Section 3.1 #4,7,16.

Turn in homework through Section 3.1 on Thursday, May 19.

*Tuesday, May 17*: Exam #3

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#### Sequences

1,1,1,1,1,1,1,1,1,1,...

1,4,9,16,25,36,49,64,81,100,...

1,3,6,10,15,12,28,36,45,55...

1,1,2,3,5,8,13,21,34,55,89...

1,1,2,3,5,8,13,21,34,55,91,...

1,1,2,2,4,2,6,4,6,4...

1,1,1,1,1,1,6,1,1,1,2,1,6,6,1,...

2,7,17,23,31,41,47,71,73,79, ...

0,0,0,0,1,1,1,1,1,2,2,2,2,2,3,3,3,3,3,4,4,4,4,4,6,6,6,6,6,7,...

12,18,20,24,30,36,40,42,48,54,...

1,11,21,1211,111221,312211,13112221,...

0,495,6174,549945,631764,...

1,1,2,1,2,2,3,1,2,2,...

#### Questions from class

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#### Random notes

There are 3 in-class exams each worth 15%.

There is a paper worth 10%.

The final exam is worth 30%.

Quizzes and Homework is worth 15%.

There may be two types of quizzes -- announced and unannounced.

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