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Kürschák Math Competition
1978 Kurschak Competition
1
1
Part of
1978 Kurschak Competition
Problems
(1)
ax^2 + by^2 = 1 infinite rational solutions if it has one
Source: 1978 Hungary - Kürschák Competition p1
10/15/2022
a
a
a
and
b
b
b
are rationals. Show that if
a
x
2
+
b
y
2
=
1
ax^2 + by^2 = 1
a
x
2
+
b
y
2
=
1
has a rational solution (in
x
x
x
and
y
y
y
), then it must have infinitely many.
algebra
number theory
rational