What is the remainder when 3^{255} is divided by 28?

Explanation

Using modulo arithmetic, we find the power of 3 closest to a multiple of 28. 3^3 = 27 \equiv -1 \pmod{28}. We rewrite 3^{255} = (3^3)^{85}. Substituting the value yields (-1)^{85} = -1 \equiv 27 \pmod{28}.

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