# 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 ...grade weights
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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Homework for our next class ...the top
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 an be the smallest positive integer so that there is a positive integer bn for which the Euclidean algorithm requires at least n steps to find the GCD of an and bn.
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 2n == 2 (mod n). Can you prove that
If 2n == 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*10400.)
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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