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Regional Mathematical Olympiad
2012 India Regional Mathematical Olympiad
2
Similar to RMO 2002
Similar to RMO 2002
Source: RMO 2012
December 2, 2012
number theory unsolved
number theory
Problem Statement
Let
a
,
b
,
c
a,b,c
a
,
b
,
c
be positive integers such that
a
∣
b
5
,
b
∣
c
5
a|b^5, b|c^5
a
∣
b
5
,
b
∣
c
5
and
c
∣
a
5
c|a^5
c
∣
a
5
. Prove that
a
b
c
∣
(
a
+
b
+
c
)
31
abc|(a+b+c)^{31}
ab
c
∣
(
a
+
b
+
c
)
31
.
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