Difference between revisions of "Number theory"
(added Pell equations) |
(Added other topics section) |
||
| Line 51: | Line 51: | ||
** [[Wilson's Theorem]] | ** [[Wilson's Theorem]] | ||
** [[Quadratic reciprocity]] | ** [[Quadratic reciprocity]] | ||
| − | |||
=== Resources === | === Resources === | ||
* [http://www.artofproblemsolving.com/Resources/Papers/SatoNT.pdf Number Theory by Naoki Sato] | * [http://www.artofproblemsolving.com/Resources/Papers/SatoNT.pdf Number Theory by Naoki Sato] | ||
| + | |||
| + | == Other Topics of Interest == | ||
| + | These are other topics that aren't particularly important for competitions and problem solving, but are good to know. | ||
| + | |||
| + | * [[Fermat's Last Theorem]] | ||
Revision as of 02:08, 23 June 2006
Number theory is the field of mathematics associated with studying the integers.
Contents
Introductory Topics
The following topics make a good introduction to number theory.
- Primes
- Composite numbers
- Divisibility
- Division Theorem (the Division Algorithm)
- Base numbers
- Diophantine equations
- Modular arithmetic
Intermediate Topics
An intermediate level of study involves many of the topics of introductory number theory, but involves an infusion of mathematical problem solving as well as algebra.
Olympiad Topics
An Olympiad level of study involves familiarity with intermediate topics to a high level, a few new topics, and a highly developed proof writing ability.
Resources
Other Topics of Interest
These are other topics that aren't particularly important for competitions and problem solving, but are good to know.
