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2008 PUMaC Algebra A10
Source:
September 24, 2019
algebra
Problem Statement
Find the sum of all integer values of
n
n
n
such that the equation
x
(
y
z
)
2
+
y
(
z
x
)
2
+
z
(
x
y
)
2
=
n
\frac{x}{(yz)^2} + \frac{y}{(zx)^2} + \frac{z}{(xy)^2} = n
(
yz
)
2
x
+
(
z
x
)
2
y
+
(
x
y
)
2
z
=
n
has a solution in positive integers.
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