What is the remainder if we divide 3^{10} by 7?

Explanation

By Fermat's Little Theorem, 3^6 \equiv 1 \pmod 7. Thus, 3^{10} = 3^6 \times 3^4 \equiv 1 \times 81 \pmod 7. Since 81 = 7 \times 11 + 4, the remainder is 4.

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