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National and Regional Contests
India Contests
Regional Mathematical Olympiad
2002 India Regional Mathematical Olympiad
3
3
Part of
2002 India Regional Mathematical Olympiad
Problems
(1)
Divides
Source: Indian RMO 2002 Problem 3
10/27/2005
Let
a
,
b
,
c
a,b,c
a
,
b
,
c
be positive integers such that
a
a
a
divides
b
2
b^2
b
2
,
b
b
b
divides
c
2
c^2
c
2
and
c
c
c
divides
a
2
a^2
a
2
. Prove that
a
b
c
abc
ab
c
divides
(
a
+
b
+
c
)
7
(a + b +c)^7
(
a
+
b
+
c
)
7
.
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