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2012 India Regional Mathematical Olympiad
2
a|b^2, b|c^2 , c|a^2 . Prove that abc|(a+b+c)^{7}
a|b^2, b|c^2 , c|a^2 . Prove that abc|(a+b+c)^{7}
Source: CRMO 2012 region 4 p2
September 30, 2018
number theory
Divisibility
divisible
powers
Problem Statement
Let
a
,
b
,
c
a,b,c
a
,
b
,
c
be positive integers such that
a
∣
b
2
,
b
∣
c
2
a|b^2, b|c^2
a
∣
b
2
,
b
∣
c
2
and
c
∣
a
2
c|a^2
c
∣
a
2
. Prove that
a
b
c
∣
(
a
+
b
+
c
)
7
abc|(a+b+c)^{7}
ab
c
∣
(
a
+
b
+
c
)
7
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