Cyclic Groups 3
Let G be a group and let a ∈ G. Prove that if a has finite order |a| = n, then for all i, j ∈ ℤ, a^i = a^j if and only if n divides i - j.
Let G be a group and let a ∈ G. Prove that if a has finite order |a| = n, then for all i, j ∈ ℤ, a^i = a^j if and only if n divides i - j.