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IberoAmerican Olympiad For University Students
2006 IberoAmerican Olympiad For University Students
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Part of
2006 IberoAmerican Olympiad For University Students
Problems
(1)
Distance between sets of fractions - OIMU 2006 Problem 1
Source:
8/30/2010
Let
m
,
n
m,n
m
,
n
be positive integers greater than
1
1
1
. We define the sets
P
m
=
{
1
m
,
2
m
,
⋯
,
m
−
1
m
}
P_m=\left\{\frac{1}{m},\frac{2}{m},\cdots,\frac{m-1}{m}\right\}
P
m
=
{
m
1
,
m
2
,
⋯
,
m
m
−
1
}
and
P
n
=
{
1
n
,
2
n
,
⋯
,
n
−
1
n
}
P_n=\left\{\frac{1}{n},\frac{2}{n},\cdots,\frac{n-1}{n}\right\}
P
n
=
{
n
1
,
n
2
,
⋯
,
n
n
−
1
}
.Find the distance between
P
m
P_m
P
m
and
P
n
P_n
P
n
, that is defined as
min
{
∣
a
−
b
∣
:
a
∈
P
m
,
b
∈
P
n
}
\min\{|a-b|:a\in P_m,b\in P_n\}
min
{
∣
a
−
b
∣
:
a
∈
P
m
,
b
∈
P
n
}
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