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Problems
Contests
National and Regional Contests
PEN Problems
PEN O Problems
10
10
Part of
PEN O Problems
Problems
(1)
O 10
Source:
5/25/2007
Let
m
≥
2
m \ge 2
m
≥
2
be an integer. Find the smallest integer
n
>
m
n>m
n
>
m
such that for any partition of the set
{
m
,
m
+
1
,
⋯
,
n
}
\{m,m+1,\cdots,n\}
{
m
,
m
+
1
,
⋯
,
n
}
into two subsets, at least one subset contains three numbers
a
,
b
,
c
a, b, c
a
,
b
,
c
such that
c
=
a
b
c=a^{b}
c
=
a
b
.