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]] | ||
| − | * [[Euler's Theorem]] | + | * [[Euler's Totient Theorem]] |
* [[Fermat's Little Theorem]] | * [[Fermat's Little Theorem]] | ||
* [[Modular arithmetic]] | * [[Modular arithmetic]] | ||
* [[Wilson's Theorem]] | * [[Wilson's Theorem]] | ||
| − | |||
| − | |||
== Olympiad Topics == | == Olympiad Topics == | ||
Revision as of 10:25, 18 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.
- Counting divisors
- Diophantine equations
- Greatest common divisor
- Least common multiple
- Modular arithmetic
- Prime factorization
- Sieve of Eratosthenes
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.
- Diophantine equations
- Euler's Totient Theorem
- Fermat's Little Theorem
- Modular arithmetic
- Wilson's Theorem
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.
