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PEN A Problems
5
A 5
A 5
Source:
May 25, 2007
conics
hyperbola
symmetry
algebra
Vieta
number theory
pen
Problem Statement
Let
x
x
x
and
y
y
y
be positive integers such that
x
y
xy
x
y
divides
x
2
+
y
2
+
1
x^{2}+y^{2}+1
x
2
+
y
2
+
1
. Show that
x
2
+
y
2
+
1
x
y
=
3.
\frac{x^{2}+y^{2}+1}{xy}=3.
x
y
x
2
+
y
2
+
1
=
3.
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