# Proving for primes

For a given prime $$p > 2$$ and positive integer $$k$$ let $S_k = 1^k + 2^k + \ldots + (p - 1)^k$

Find those values of $$k$$ for which $$p \, |\, S_k$$.

Note by Department 8
2 years, 5 months ago

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all values of $$k$$ such that $$p-1$$ does not divide $$k$$.

- 2 years, 4 months ago

Some solutions are k=1,2,3,p

- 2 years, 5 months ago

k should not be the multiple of $$\phi (p)$$ will always satisfy.

- 2 years, 5 months ago