Calculate $1^{30} + 2^{30} + 3^{30} + \ldots + 17^{30} \mod 31$
Using Fermat's Theorem: $$ 1^{30} = 1 \mod 31, $$ (since $31$ is prime). This implies the above is congruent to $17 \mod 31$
This is correct, right?
Calculate $1^{30} + 2^{30} + 3^{30} + \ldots + 17^{30} \mod 31$
Using Fermat's Theorem: $$ 1^{30} = 1 \mod 31, $$ (since $31$ is prime). This implies the above is congruent to $17 \mod 31$
This is correct, right?
True. But 1^n=1 mod whatever. Fermat's Little Theorem says that n^30=1 for all n prime to 31. So your answer of 17 is correct.