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1987 IMO Longlists
77
IMO LongList 1987 - Find the least positive integer k
IMO LongList 1987 - Find the least positive integer k
Source:
September 6, 2010
inequalities
function
inequalities unsolved
Problem Statement
Find the least positive integer
k
k
k
such that for any
a
∈
[
0
,
1
]
a \in [0, 1]
a
∈
[
0
,
1
]
and any positive integer
n
,
n,
n
,
a
k
(
1
−
a
)
n
<
1
(
n
+
1
)
3
.
a^k(1 - a)^n < \frac{1}{(n+1)^3}.
a
k
(
1
−
a
)
n
<
(
n
+
1
)
3
1
.
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