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Netherlands Contests
Dutch Mathematical Olympiad
1977 Dutch Mathematical Olympiad
1
diophantine 2x^2y = (x+2)^2(y + 1)> 1000
diophantine 2x^2y = (x+2)^2(y + 1)> 1000
Source: Netherlands - Dutch NMO 1977 p1
January 28, 2023
number theory
diophantine
Diophantine equation
Problem Statement
Solve, for integers
x
x
x
and
y
y
y
:
2
x
2
y
=
(
x
+
2
)
2
(
y
+
1
)
,
2x^2y = (x+2)^2(y + 1),
2
x
2
y
=
(
x
+
2
)
2
(
y
+
1
)
,
provided that
(
x
+
2
)
2
(
y
+
1
)
>
1000
(x+2)^2(y + 1)> 1000
(
x
+
2
)
2
(
y
+
1
)
>
1000
.
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