MTH 346 (646) Elmentary Number Theory II
Dr. Elmer K. Hayashi
 Fall 2001
Assignments

Aug 29-31 Sep 3-7 Sep 10-14 Sep 17-21 Sep 24-28
Oct 1-5 Oct 8-12 Oct 15-19 Oct 22-26 Oct 29-Nov 2
Nov 5-9 Nov 12-16 Nov 19-23 Nov 26-30 Dec 3-7

Textbook: David M. Burton, Elementary Number Theory, Fourth Edition
Wed, 08/29/2001. Perfect Numbers
Characterization of all even perfect numbers.
Read section 10.1,
Do problems 1,2, and 5 on page 204.
 
Fri, 08/31/2001. Mersenne numbers and primes.
Even perfect numbers end in 6 or 28. A perfect square cannot be a perfect number.
Mon, 09/03/2001. Prime Divisors of Even Perfect Numbers.
Characterization of the prime factors of even perfect numbers. An algorithm for determining if a Mersenne number is prime or composite.
 
 
Wed, 09/05/2001. Odd Perfect Numbers.
The form of an odd perfect number if one exists.
 
Fri, 09/07/2001. Fermat Numbers.
If 2^m+1 is prime, then m is a power of 2. Two distinct Fermat numbers are relatively prime, and hence there must be infinitely many prime numbers.
Mon, 09/10/2001. Pepin's Test.
Pepin's test for the primality of a Fermat number, and a characterization of prime factors of Fermat numbers.
On pages 221-222, do problems 4, 9, 17.
 
 
Wed, 09/12/2001. Cryptography.
RSA Cryptosystem, an example of a public-key cryptosystem.
Do problems 5-8 on page 149.
 
Fri, 09/14/2001.
No class.
Mon, 09/17/2001. Knapsack Cryptosystem.
A quick look at a second example of a public-key cryptosystem. Review of problems on Fermat numbers and primes.
 
Wed, 09/19/2001. Sums of Two Squares.
Characterization of all positive integers that can be written as the sum of two squares.
 
Fri, 09/21/2001. Sums of Four Squares.
Every positive integer can be written as the sum of four squares.
Mon, 09/24/2001. Approximations by Rationals with Least Denominator.
An algorithm for approximating a real number by rationals with least denominator. Farey fractions, and the mediant between two sufficiently close fractions.
 
Tue, 09/25/2001. Continued Fractions.
An algorithm for computing the finite continued fraction expansion of a rational number. The sequence of convergents.
 
Wed, 09/26/2001.
 
Fri, 09/28/2001.
Mon, 10/01/2001.
 
Tue, 10/02/2001.
 
Wed, 10/03/2001.
 
Fri, 10/05/2001.
Mon, 10/08/2001.
 
Tue, 10/09/2001.
 
Wed, 10/10/2001.
 
Fri, 10/12/2001.
Mon,10/15/2001.
 
Tue, 10/16/2001.
 
Wed, 10/17/2001.
 
Fri, 10/19/2001. Fall Break.
No Class.
Mon, 10/22/2001.
 
Tue, 10/23/2001.
 
Wed, 10/24/2001.
 
Fri, 10/26/2001.
Mon, 10/29/2001.
 
Tue, 10/30/2001.
 
Wed, 10/31/2001.
 
Fri, 11/02/2001.
Mon, 11/05/2001.
 
Tue, 11/06/2001.
 
Wed, 11/07/2001.
 
Fri, 11/09/2001.
Mon, 11/12/2001.
 
Tue, 11/13/2001.
 
Wed, 11/14/2001.
 
Fri, 11/16/2001.
Mon, 11/19/2001.
 
Tue, 11/20/2001.
 
Wed, 11/21/2001. Thanksgiving Vacation.
No Class.
Mon, 11/26/2001.
 
Tue, 11/27/2001.
 
Wed, 11/28/2001.
 
Fri, 11/30/2001.
Mon, 12/03/2001.
 
Tue, 12/04/2001.
 
Wed, 12/05/2001.
 
Fri, 12/07/2001.
 
Friday, 12/14/2001. Final Examination.
2:00 p.m.-5:00 p.m.
Calloway 113.

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Created 05/31/2001. Last modified 05/31/2001. Email to ekh@wfu.edu