Compute 2^4 mod 5.

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Prepare for the AMSOC 26-003 Module A Test. Utilize flashcards and multiple choice questions with hints and explanations. Ace your exam!

Multiple Choice

Compute 2^4 mod 5.

Explanation:
Modular arithmetic lets you reduce the remainder as you multiply. With modulus 5, the powers of 2 follow a short cycle: 2, 4, 3, 1, and then repeat. After four multiplications, you land on 1, so 2^4 ≡ 1 (mod 5). You can also see it by squaring: 2^2 ≡ 4, then (2^2)^2 ≡ 4^2 = 16 ≡ 1 (mod 5). Therefore the remainder when dividing 2^4 by 5 is 1.

Modular arithmetic lets you reduce the remainder as you multiply. With modulus 5, the powers of 2 follow a short cycle: 2, 4, 3, 1, and then repeat. After four multiplications, you land on 1, so 2^4 ≡ 1 (mod 5). You can also see it by squaring: 2^2 ≡ 4, then (2^2)^2 ≡ 4^2 = 16 ≡ 1 (mod 5). Therefore the remainder when dividing 2^4 by 5 is 1.

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