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Balkan MO
2007 Balkan MO
3
3
Part of
2007 Balkan MO
Problems
(1)
Many square roots, but rational !
Source: Balkan Olympiad 2007,problem 3
4/28/2007
Find all positive integers
n
n
n
such that there exist a permutation
σ
\sigma
σ
on the set
{
1
,
2
,
3
,
…
,
n
}
\{1,2,3, \ldots, n\}
{
1
,
2
,
3
,
…
,
n
}
for which
σ
(
1
)
+
σ
(
2
)
+
…
+
σ
(
n
−
1
)
+
σ
(
n
)
\sqrt{\sigma(1)+\sqrt{\sigma(2)+\sqrt{\ldots+\sqrt{\sigma(n-1)+\sqrt{\sigma(n)}}}}}
σ
(
1
)
+
σ
(
2
)
+
…
+
σ
(
n
−
1
)
+
σ
(
n
)
is a rational number.
algebra
polynomial
floor function
induction
number theory unsolved
number theory