a² Prove that if ged(a, m); 1 and gcd (a-1, m)=1, then 1+a+a² + ... + a(m) = 0 (mod m). (Hint: What do you get when you multiply the congruence by a-1?)

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.1: Real Numbers
Problem 5E
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a²
Prove that if ged(a, m); 1 and gcd (a-1, m)=1,
then 1+a+a² + ... + a(m) = 0 (mod m). (Hint:
What do you get when you multiply the
congruence by a-1?)
Transcribed Image Text:a² Prove that if ged(a, m); 1 and gcd (a-1, m)=1, then 1+a+a² + ... + a(m) = 0 (mod m). (Hint: What do you get when you multiply the congruence by a-1?)
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