Calculate $1^{30} + 2^{30} + 3^{30} + \ldots + 17^{30} \mod 31$

Calculate $1^{30} + 2^{30} + 3^{30} + \ldots + 17^{30} \mod 31$

Using Fermat is Theorem:. $$ 1^{30} = 1 \mod 31, $$ (given that $31$ is prime). This indicates the above is conforming to $17 \mod 31$

This is proper, appropriate?

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2019-05-18 21:58:04
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Answers: 1

True. Yet 1 ^ n = 1 mod whatever. Fermat is Little Theorem claims that n ^ 30 = 1 for all n prime to 31. So your solution of 17 is proper.

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2019-05-21 21:25:53
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