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Find the remainder when 3^{2001} is divided by 7.

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Stage: 5 Challenge Level: Challenge Level:1

In modulus arithmetic the only numbers involved are the whole numbers 0 to $m-1$ where $m$ is the modulus (or if you prefer it 1 to $m$). The multiplicative inverse of 7 (mod 26) is the number (equivalent to 1/7) that 7 is multiplied by to get the answer 1. The additive inverse of 17 is the number you add to 17 to get the answer 0 (mod 26).