◀ ▲ ▶Branches / Numbertheory / Section: Algebraic Structures of Reduced Residue Systems
Section: Algebraic Structures of Reduced Residue Systems
In this section, we will introduce reduced residue systems, i.e. sets of integers which represent only those congruence classes modulo a positive integer $m > 0,$ which are coprime to $m.$
We will also study their algebraic structure for prime and composite modules $m.$ Furthermore, we will prove theorems which characterize prime numbers, in particular, the Fermat's little theorem, as well as the Wilson's theorem.
Table of Contents
 Definition: Reduced Residue System
 Proposition: Creation of Reduced Residue Systems From Others
 Proposition: Existence and Number of Solutions of Congruence With One Variable
 Proposition: Multiplicative Group Modulo an Integer $(\mathbb Z_m^*,\cdot)$
 Theorem: EulerFermat Theorem
 Proposition: A Necessary Condition for an Integer to be Prime
 Proposition: Wilson's Condition for an Integer to be Prime
 Proposition: Complete and Reduced Residue Systems (Revised)
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