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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 $m.$

| | | | created: 2019-04-19 06:41:31 | modified: 2019-06-22 08:34:02 | by: bookofproofs | references: [1272], [8152]

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

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Bibliography (further reading)

[8152] Jones G., Jones M.: “Elementary Number Theory (Undergraduate Series)”, Springer, 1998

[1272] Landau, Edmund: “Vorlesungen ├╝ber Zahlentheorie, Aus der Elementaren Zahlentheorie”, S. Hirzel, Leipzig, 1927

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