Let k be the order of "a" in n mode, then prove that, o(ah) = k <=> (h, k) = 1

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.5: Permutations And Inverses
Problem 4E: 4. Let , where is nonempty. Prove that a has left inverse if and only if for every subset of .
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a' nın n modunda mertebesi k olsun. O halde ,
o(a^h)= k  <=> (h,k)=1   olduğunu ispatla.
(It's number theory)
(please can you solve that step by step)

Let k be the order of "a" in n mode, then prove that ,
o(a") = k <=> (h, k) = 1
Transcribed Image Text:Let k be the order of "a" in n mode, then prove that , o(a") = k <=> (h, k) = 1
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