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1979 IMO Longlists
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55
Part of
1979 IMO Longlists
Problems
(1)
Diophantine - Coprime - Infinite solutions proof
Source: ILL 1979 - Problem 55
6/5/2011
Let
a
,
b
a,b
a
,
b
be coprime integers. Show that the equation
a
x
2
+
b
y
2
=
z
3
ax^2 + by^2 =z^3
a
x
2
+
b
y
2
=
z
3
has an infinite set of solutions
(
x
,
y
,
z
)
(x,y,z)
(
x
,
y
,
z
)
with
{
x
,
y
,
z
}
ā
Z
\{x,y,z\}\in\mathbb{Z}
{
x
,
y
,
z
}
ā
Z
and each pair of
x
,
y
x,y
x
,
y
mutually coprime.
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