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Let U(n) be the group of units in Zn. If n > 2, prove that there is an element k EU (n) such chat k² = 1 and k # 1.

Let U(n) be the group of units in Zn. If n > 2, prove that there is an element k EU (n) such chat k² = 1 and k # 1.

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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Please go though every step and do not use a texblook solution.

Why is the gcd(n-1,n)=1? 

why is n-1 an element if U(n)?

Example let K = n-1

Assume since n-1 is an element of Zn, K is an element of Zn

let the gcd (n, n-1)= q

Prove somethign like this dont just jump to the gcd(n-1,n)=1 therefore n-1 is an element of U(n) so (n-1)^2 is congruent to n^2 - n2+1modn, 

I know the answer, I'm looking for proof with an explination with each step. 

Let U(n) be the group of units in Zn. If n > 2, prove that there is an element k = U(n) such that k2 = 1 and k 1.
Transcribed Image Text:Let U(n) be the group of units in Zn. If n > 2, prove that there is an element k = U(n) such that k2 = 1 and k 1.
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