Section: Algebraic Structures of Complete Residue Systems

In the following section we will introduce complete residue systems, i.e. sets of integers which represent all possible congruence classes modulo a positive integer $m > 0.$ We will also study their algebraic structure for prime and composite modules $m.$

new:branchproposition:Field implies $n$ prime

The previous proposition has shown that if $p$ is prime, then $\mathbb Z_p$ is a finite field.

  1. Definition: Complete Residue System
  2. Proposition: Addition, Subtraction and Multiplication of Congruences, the Commutative Ring $\mathbb Z_m$
  3. Proposition: Cancellation of Congruences With Factor Co-Prime To Module, Field $\mathbb Z_p$
  4. Proposition: Cancellation of Congruences with General Factor
  5. Proposition: Creation of Complete Residue Systems From Others

Parts: 1

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  1. Landau, Edmund: "Vorlesungen über Zahlentheorie, Aus der Elementaren Zahlentheorie", S. Hirzel, Leipzig, 1927
  2. Jones G., Jones M.: "Elementary Number Theory (Undergraduate Series)", Springer, 1998