MathDB

Distance between sets of fractions - OIMU 2006 Problem 1

Source:

August 30, 2010

modular arithmeticnumber theory proposednumber theory

Problem Statement

Let

m,n

be positive integers greater than

1

. We define the sets

P_m=\left\{\frac{1}{m},\frac{2}{m},\cdots,\frac{m-1}{m}\right\}

and

P_n=\left\{\frac{1}{n},\frac{2}{n},\cdots,\frac{n-1}{n}\right\}

.
Find the distance between

P_m

and

P_n

, that is defined as

\min\{|a-b|:a\in P_m,b\in P_n\}