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2011 JBMO Shortlist
3
y^2 + xy + 3x = n(x^2 + xy + 3y)
y^2 + xy + 3x = n(x^2 + xy + 3y)
Source: JBMO 2011 Shortlist N3
October 14, 2017
JBMO
number theory
Problem Statement
Find all positive integers
n
n
n
such that the equation
y
2
+
x
y
+
3
x
=
n
(
x
2
+
x
y
+
3
y
)
y^2 + xy + 3x = n(x^2 + xy + 3y)
y
2
+
x
y
+
3
x
=
n
(
x
2
+
x
y
+
3
y
)
has at least a solution
(
x
,
y
)
(x, y)
(
x
,
y
)
in positive integers.
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