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The least non-negative remainder when $3^{51}$ is divided by 7 is: |
2 3 6 5 |
6 |
The correct answer is Option (3) → 6 $3^6=729.$ $729 \equiv 1 \pmod{7}.$ $3^{51}=(3^6)^8\cdot3^3.$ $3^{51}\equiv1^8\cdot27\pmod{7}.$ $27\equiv6\pmod{7}.$ $6.$ |
