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Prove that for any integer a, [a]=m = [r]=m where r is the unique remainder when a is divided by m, and thus, A/ =m = {[0]=m [1]=m .. [m – 1]=m} =: Zm- %3D

Prove that for any integer a, [a]=m = [r]=m where r is the unique remainder when a is divided by m, and thus, A/ =m = {[0]=m [1]=m .. [m – 1]=m} =: Zm- %3D

Advanced Engineering Mathematics
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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Prove that for any integer a, [a]=m = [r]=m where r is the unique remainder when a is divided by m, and thus, A/ =m = {[0]=m [1]=m; .. [m – 1]=m} =: Zm. %3D
Transcribed Image Text:Prove that for any integer a, [a]=m = [r]=m where r is the unique remainder when a is divided by m, and thus, A/ =m = {[0]=m [1]=m; .. [m – 1]=m} =: Zm. %3D
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