In modular arithmetic, find 3^4 mod 5.

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Multiple Choice

In modular arithmetic, find 3^4 mod 5.

Explanation:
In modular arithmetic, you reduce at each multiplication step by the modulus. So modulo 5, replace numbers by their remainders and keep going. Compute 3^2: 3^2 = 9 ≡ 4 (mod 5). Then 3^4 = (3^2)^2 ≡ 4^2 = 16 ≡ 1 (mod 5). Therefore, 3^4 leaves a remainder of 1 when divided by 5. You can also see the sequence of residues: 3^1 ≡ 3, 3^2 ≡ 4, 3^3 ≡ 2, 3^4 ≡ 1, which confirms the result.

In modular arithmetic, you reduce at each multiplication step by the modulus. So modulo 5, replace numbers by their remainders and keep going.

Compute 3^2: 3^2 = 9 ≡ 4 (mod 5). Then 3^4 = (3^2)^2 ≡ 4^2 = 16 ≡ 1 (mod 5). Therefore, 3^4 leaves a remainder of 1 when divided by 5.

You can also see the sequence of residues: 3^1 ≡ 3, 3^2 ≡ 4, 3^3 ≡ 2, 3^4 ≡ 1, which confirms the result.

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