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3
IMEO 2017 Problem 3
IMEO 2017 Problem 3
Source: IMEO
September 28, 2017
number theory
IMEO
Problem Statement
A triple
(
x
,
y
,
z
)
(x,y,z)
(
x
,
y
,
z
)
of real numbers is called a superparticular if
x
+
1
x
⋅
y
+
1
y
=
z
+
1
z
\frac{x+1}{x} \cdot \frac{y+1}{y}=\frac{z+1}{z}
x
x
+
1
⋅
y
y
+
1
=
z
z
+
1
Find all superparticular positive integer triples.
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