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2013 JBMO Shortlist
5
\frac{1}{x^2}+\frac{y}{xz}+\frac{1}{z^2}=\frac{1}{2013}
\frac{1}{x^2}+\frac{y}{xz}+\frac{1}{z^2}=\frac{1}{2013}
Source: JBMO Shortlist 2013 NT5
April 24, 2019
number theory
Diophantine equation
positive integers
Problem Statement
Solve in positive integers:
1
x
2
+
y
x
z
+
1
z
2
=
1
2013
\frac{1}{x^2}+\frac{y}{xz}+\frac{1}{z^2}=\frac{1}{2013}
x
2
1
+
x
z
y
+
z
2
1
=
2013
1
.
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