Let G = 1,2,3,4,5,6}. Find the order of all the elements of G under the binary operation“multiplioation modulo 7”
Question
Solution 1
To find the order of all the elements of G under the binary operation "multiplication modulo 7", we need to find the smallest positive integer n such that a^n ≡ 1 (mod 7) for each a in G.
- For a = 1, 1^n ≡ 1 (mod 7) for all n, so the order of 1 is 1.
- For a = 2, we find that 2^3 ≡ 1 (mod 7), s Knowee AI is a powerful AI-powered study tool designed to help you to solve study problem.
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