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Problem 2 - Entrance Test

What is the remainder when 2^2023 is divided by 7?

Correct: B

The powers of 2 modulo 7 cycle with period 3: 2^1 mod 7 = 2, 2^2 mod 7 = 4, 2^3 mod 7 = 1, 2^4 mod 7 = 2, etc. Since 2023 = 3 * 674 + 1, 2^2023 mod 7 = 2^1 mod 7 = 2.