MathDB

Find the values of k

Source: Hungary-Israel Binational Olympiad 2009, Problem 1

August 17, 2009

modular arithmeticalgebrapolynomialnumber theoryrelatively primenumber theory unsolved

Problem Statement

For a given prime

p > 2

and positive integer

k

let S_k \equal{} 1^k \plus{} 2^k \plus{} \ldots \plus{} (p \minus{} 1)^k Find those values of

k

for which

p \, |\, S_k