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(1+a^2)(1+b^2)(1+c^2) is perfect square-[UKRMO 2009 Grade 8]
(1+a^2)(1+b^2)(1+c^2) is perfect square-[UKRMO 2009 Grade 8]
Source:
January 21, 2011
Problem Statement
Let
a
,
b
,
c
a, b, c
a
,
b
,
c
be integers satisfying
a
b
+
b
c
+
c
a
=
1.
ab + bc + ca = 1.
ab
+
b
c
+
c
a
=
1.
Prove that
(
1
+
a
2
)
(
1
+
b
2
)
(
1
+
c
2
)
(1+ a^2 )(1+ b^2 )(1+ c^2 )
(
1
+
a
2
)
(
1
+
b
2
)
(
1
+
c
2
)
is a perfect square.
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