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.

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.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 32EQ

See similar textbooks