MathDB

Problem 8 of Third round

Source: I International Festival of Young Mathematicians Sozopol 2010, Theme for 10-12 grade

December 14, 2019

number theorymodulo

Problem Statement

Let

m, n,

and

k

be natural numbers, where

n

is odd. Prove that

\frac{1}{m}+\frac{1}{m+n}+...+\frac{1}{m+kn}

is not a natural number.