MathDB

M / 2004 < k / n < (m + 1) / 2005

Source: 7th German TST 2005, problem 1

May 30, 2005

Putnaminequalitiesnumber theory unsolvednumber theory

Problem Statement

Find the smallest positive integer

n

with the following property:
For any integer

m

with

0 < m < 2004

, there exists an integer

k

such that

\frac{m}{2004}<\frac{k}{n}<\frac{m+1}{2005}.