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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 co-prime 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.