MathDB

Let

n > 1

be an integer, and

n

can divide 2^{\phi(n)} \plus{} 3^{\phi(n)} \plus{} \cdots \plus{} n^{\phi(n)}, let

p_{1},p_{2},\cdots,p_{k}

be all distinct prime divisors of

n

. Show that \frac {1}{p_{1}} \plus{} \frac {1}{p_{2}} \plus{} \cdots \plus{} \frac {1}{p_{k}} \plus{} \frac {1}{p_{1}p_{2}\cdots p_{k}} is an integer. ( where

\phi(n)

is defined as the number of positive integers

\leq n

that are relatively prime to

n

Problem Statement