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Indonesia MO
2010 Indonesia MO
4
4
Part of
2010 Indonesia MO
Problems
(1)
Indonesia National Science Olympiad 2010 - Day 1 Problem 4
Source:
9/28/2010
Given that
m
m
m
and
n
n
n
are positive integers with property:
(
m
n
)
∣
(
m
2010
+
n
2010
+
n
)
(mn)\mid(m^{2010}+n^{2010}+n)
(
mn
)
∣
(
m
2010
+
n
2010
+
n
)
Show that there exists a positive integer
k
k
k
such that
n
=
k
2010
n=k^{2010}
n
=
k
2010
Nanang Susyanto, Yogyakarta
number theory unsolved
number theory