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Bulgaria National Olympiad
2005 Bulgaria National Olympiad
1
Bulguaria 1
Bulguaria 1
Source: BMO Problem 1
May 15, 2005
number theory proposed
number theory
Problem Statement
Determine all triples
(
x
,
y
,
z
)
\left( x,y,z\right)
(
x
,
y
,
z
)
of positive integers for which the number
2005
x
+
y
+
2005
y
+
z
+
2005
z
+
x
\sqrt{\frac{2005}{x+y}}+\sqrt{\frac{2005}{y+z}}+\sqrt{\frac{2005}{z+x}}
x
+
y
2005
+
y
+
z
2005
+
z
+
x
2005
is an integer .
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