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1985 IMO Longlists
68
nice
nice
Source: very nice
September 18, 2006
number theory unsolved
number theory
Problem Statement
Show that the sequence
{
a
n
}
n
≥
1
\{a_n\}_{n\geq1}
{
a
n
}
n
≥
1
defined by
a
n
=
[
n
2
]
a_n = [n \sqrt 2]
a
n
=
[
n
2
]
contains an infinite number of integer powers of
2
2
2
. (
[
x
]
[x]
[
x
]
is the integer part of
x
x
x
.)
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