×

# 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 Lakshya Sinha
11 months, 1 week ago

Sort by:

all values of $$k$$ such that $$p-1$$ does not divide $$k$$. · 10 months, 3 weeks ago

Some solutions are k=1,2,3,p · 11 months, 1 week ago

k should not be the multiple of $$\phi (p)$$ will always satisfy. · 11 months, 1 week ago