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2000 Mongolian Mathematical Olympiad
Problem 1
range of (x+y+z)^2/xyz, x,y,z in N
range of (x+y+z)^2/xyz, x,y,z in N
Source: Mongolia MO 2000 Teachers P1
April 22, 2021
number theory
Problem Statement
Find all integers that can be written in the form
(
x
+
y
+
z
)
2
x
y
z
\frac{(x+y+z)^2}{xyz}
x
yz
(
x
+
y
+
z
)
2
, where
x
,
y
,
z
x,y,z
x
,
y
,
z
are positive integers.
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