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This questions is driving me crazy!   Show that if a, b, k, and m are integers such that k ≥ 1, m ≥ 2, and a ≡ b (mod m), then a^k ≡ b^k (mod m)

In Russia you get into a bus, take a ticket, and sometimes say : Wow, a lucky number! Bus tickets are numbered by 6-digit numbers, and a lucky ticket has the sum of 3 first digits being equal to the...