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Austria Contests
Austrian MO Beginners' Competition
2004 Austria Beginners' Competition
2
2
Part of
2004 Austria Beginners' Competition
Problems
(1)
x^2+5y^2-6\leq \sqrt{(x^2-2)(y^2-0.04)} integers
Source: 2004 Austria Beginners' Competition p2
10/4/2022
For what pairs of integers
(
x
,
y
)
(x,y)
(
x
,
y
)
does the inequality
x
2
+
5
y
2
−
6
≤
(
x
2
−
2
)
(
y
2
−
0.04
)
x^2+5y^2-6\leq \sqrt{(x^2-2)(y^2-0.04)}
x
2
+
5
y
2
−
6
≤
(
x
2
−
2
)
(
y
2
−
0.04
)
hold?
number theory
inequalities
diophantine