MathDB

3

Part of 2005 IberoAmerican

Problems(1)

\sum{i^{-p}} = 0 mod p^3

Source:

9/28/2005
Let p>3p > 3 be a prime. Prove that if ∑i=1p−11ip=nm, \sum_{i=1 }^{p-1}{1\over i^p} = {n\over m}, with \gdc(n,m) = 1, then p3p^3 divides nn.
modular arithmeticalgebranumber theoryDivisibility