View source for Number theory/Introduction

[[Number theory]] is the study of [[integers]] and an introductory study of number theory involves exploring many common relationships between integers.


== Introductory Topics in Number Theory ==
The following topics make a good introduction to [[number theory]]:
* [[Prime number | Primes]]
** [[Sieve of Eratosthenes]]
** [[Prime factorization]]
* [[Composite number | Composite numbers]]
* [[Divisibility]]
** [[Divisor]]s
*** [[Common divisor]]s
**** [[Greatest common divisor]]s
*** [[Counting divisors]]
** [[Multiple]]s
*** [[Common multiple]]s
**** [[Least common multiple]]s
* [[Division Theorem]] (the Division Algorithm)
* [[Base numbers]]
* [[Diophantine equation | Diophantine equations]]
** [[Simon's Favorite Factoring Trick]]
* [[Modular arithmetic]]
** [[Linear congruence]]

== Introductory Number Theory Resources ==
=== Books ===
* ''the Art of Problem Solving Introduction to Number Theory'' by [[Mathew Crawford]] [http://www.artofproblemsolving.com/Books/AoPS_B_Item.php?page_id=10 (details)]
* General Interest
** ''Fermat's Enigma'' by Simon Singh [http://www.amazon.com/exec/obidos/ASIN/0385493622/artofproblems-20 (details)]
** ''Music of the Primes'' by Marcus du Sautoy [http://www.amazon.com/exec/obidos/ASIN/0066210704/artofproblems-20 (details)]

=== Classes ===
* [[Introduction to Number Theory Course]] is part of the [[AoPS Online School]].  [http://www.artofproblemsolving.com/Classes/AoPS_C_ClassesS.php#begnum Details]



== See also ==
* [[Number theory/Intermediate | Intermediate number theory]]
* [[Number theory/Olympiad | Olympiad number theory]]


[[Category:Introductory Mathematics Topics]]
[[Category:Number theory]]