The following is written in my mathematical proofs book "Z4 consists of the four classes (sets of integers) [0],[1],[2],[3], where for r ∈ {0, 1, 2, 3}, [r] = {3q + r : q ∈ Z}" Im confused on why it's 3q+r and not 4q+r, I know there is a general rule but i cannot find it, I know why it consists of 4 classes, but somehow i dont get the "{3q + r : q ∈ Z}" part, please explain step by step.

The following is written in my mathematical proofs book "Z4 consists of the four classes (sets of integers) [0],[1],[2],[3], where for r ∈ {0, 1, 2, 3}, [r] = {3q + r : q ∈ Z}" Im confused on why it's 3q+r and not 4q+r, I know there is a general rule but i cannot find it, I know why it consists of 4 classes, but somehow i dont get the "{3q + r : q ∈ Z}" part, please explain step by step.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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