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diophantine 2xy^2 + x + y + 1 = x^2 + 2y^2 + xy (HOMC 2015 J Q14)
diophantine 2xy^2 + x + y + 1 = x^2 + 2y^2 + xy (HOMC 2015 J Q14)
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August 6, 2019
Diophantine equation
number theory
diophantine
Problem Statement
Determine all pairs of integers
(
x
,
y
)
(x, y)
(
x
,
y
)
such that
2
x
y
2
+
x
+
y
+
1
=
x
2
+
2
y
2
+
x
y
2xy^2 + x + y + 1 = x^2 + 2y^2 + xy
2
x
y
2
+
x
+
y
+
1
=
x
2
+
2
y
2
+
x
y
.
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