9. Let m and a be integers such that m > 1 and (a,m)= 1. Prove that if {r1, ...,r(m)} is a reduced set of residues modulo m, then {arı,..., arp(m)} is also a reduced set of residues modulo m.
9. Let m and a be integers such that m > 1 and (a,m)= 1. Prove that if {r1, ...,r(m)} is a reduced set of residues modulo m, then {arı,..., arp(m)} is also a reduced set of residues modulo m.
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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Transcribed Image Text:9. Let m and a be integers such that m≥ 1 and (a,m) = 1. Prove
that if {r₁, ..., p(m)} is a reduced set of residues modulo m, then
{ar₁,..., arp(m)} is also a reduced set of residues modulo m.
Expert Solution

Step 1: Explanation
Consider that is a complete set of residues modulo m.
It is given that gcd ( a,m) = 1
The objective is to claim that is a complete set of residues modulo m
We know that any set of integers form a complete set of residues modulo m if and only if all the integers are congruent to different integer modulo m.
That is is a complete set of residues modulo m.Then, ai
1
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