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National and Regional Contests
PEN Problems
PEN A Problems
1
1
Part of
PEN A Problems
Problems
(1)
A 1
Source:
5/25/2007
Show that if
x
,
y
,
z
x, y, z
x
,
y
,
z
are positive integers, then
(
x
y
+
1
)
(
y
z
+
1
)
(
z
x
+
1
)
(xy+1)(yz+1)(zx+1)
(
x
y
+
1
)
(
yz
+
1
)
(
z
x
+
1
)
is a perfect square if and only if
x
y
+
1
xy+1
x
y
+
1
,
y
z
+
1
yz+1
yz
+
1
,
z
x
+
1
zx+1
z
x
+
1
are all perfect squares.
quadratics
Vieta
algebra
ratio
number theory
relatively prime
pen