MathDB

looks like Fedor's russian problem

Source: Bulgarian Math Olympiad MO 2004, problem 2

May 17, 2004

number theory unsolvednumber theory

Problem Statement

For any positive integer

n

the sum

\displaystyle 1+\frac 12+ \cdots + \frac 1n

is written in the form

\displaystyle \frac{P(n)}{Q(n)}

, where

P(n)

and

Q(n)

are relatively prime. a) Prove that

P(67)

is not divisible by 3; b) Find all possible

n

, for which

P(n)

is divisible by 3.