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Poland - Second Round
2007 Poland - Second Round
1
Polish MO 2007 Second Round Day 2, problem 1
Polish MO 2007 Second Round Day 2, problem 1
Source:
February 28, 2007
Problem Statement
a
a
a
,
b
b
b
,
c
c
c
,
d
d
d
are positive integers and
a
d
=
b
2
+
b
c
+
c
2
ad=b^{2}+bc+c^{2}
a
d
=
b
2
+
b
c
+
c
2
Prove that
a
2
+
b
2
+
c
2
+
d
2
a^{2}+b^{2}+c^{2}+d^{2}
a
2
+
b
2
+
c
2
+
d
2
is a composed number.
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