Difference between revisions of "Number theory"
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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]]. | 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]]. | ||
* [[Diophantine equations]] | * [[Diophantine equations]] | ||
| + | ** [[Pell equation | Pell equations]] | ||
** [[Simon's Favorite Factoring Trick]] | ** [[Simon's Favorite Factoring Trick]] | ||
* [[Euclidean algorithm]] | * [[Euclidean algorithm]] | ||
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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]] | ||
| + | ** [[Pell equation | Pell equations]] | ||
** [[Simon's Favorite Factoring Trick]] | ** [[Simon's Favorite Factoring Trick]] | ||
* [[Modular arithmetic]] | * [[Modular arithmetic]] | ||
Revision as of 16:55, 22 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.
- 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.
