Difference between revisions of "Number theory"
(added SFFT internal links) |
(rewrote much of Olympiad Topics) |
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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. | 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. | ||
* [[Diophantine equations]] | * [[Diophantine equations]] | ||
| − | * | + | ** [[Simon's Favorite Factoring Trick]] |
| − | * [[ | ||
* [[Modular arithmetic]] | * [[Modular arithmetic]] | ||
| − | * [[Wilson's Theorem]] | + | ** [[Linear congruence]] |
| + | *** [[Chinese Remainder Theorem]] | ||
| + | ** [[Euler's Totient Theorem]] | ||
| + | ** [[Fermat's Little Theorem]] | ||
| + | ** [[Wilson's Theorem]] | ||
| + | ** [[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] | ||
Revision as of 22:38, 19 June 2006
Number theory is the field of mathematics associated with studying the integers.
Introductory Topics
The following topics make a good introduction to number theory.
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.
