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solve in integers: x^2-y^2=z and 3xy+(x-y)z=z^2
solve in integers: x^2-y^2=z and 3xy+(x-y)z=z^2
Source: JBMO Shortlist 2013 NT6
April 24, 2019
number theory
Diophantine Equations
Integers
Problem Statement
Solve in integers the system of equations:
x
2
−
y
2
=
z
x^2-y^2=z
x
2
−
y
2
=
z
3
x
y
+
(
x
−
y
)
z
=
z
2
3xy+(x-y)z=z^2
3
x
y
+
(
x
−
y
)
z
=
z
2
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