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Japan MO Finals
1994 Japan MO Finals
1
1
Part of
1994 Japan MO Finals
Problems
(1)
Sequence (c_n) that does not cross with sequence (b_n)
Source: Japanese MO Finals 1994
2/11/2011
For any positive integer
n
n
n
, let
a
n
a_n
a
n
denote the closest integer to
n
\sqrt{n}
n
, and let
b
n
=
n
+
a
n
b_n=n+a_n
b
n
=
n
+
a
n
. Determine the increasing sequence
(
c
n
)
(c_n)
(
c
n
)
of positive integers which do not occur in the sequence
(
b
n
)
(b_n)
(
b
n
)
.
number theory unsolved
number theory