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