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Hanoi Open Mathematics Competition
2015 Hanoi Open Mathematics Competitions
14
14
Part of
2015 Hanoi Open Mathematics Competitions
Problems
(1)
diophantine 2xy^2 + x + y + 1 = x^2 + 2y^2 + xy (HOMC 2015 J Q14)
Source:
8/6/2019
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
.
Diophantine equation
number theory
diophantine