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Purple Comet Problems
2016 Purple Comet Problems
28
Purple Comet 2016 HS Problem 28
Purple Comet 2016 HS Problem 28
Source:
April 12, 2018
Purple Comet
Problem Statement
Find the sum of all the possible values of xy such that x and y are positive integers satisfying
(
x
2
+
1
)
(
y
2
+
1
)
+
2
(
x
−
y
)
(
1
−
x
y
)
=
4
(
1
+
x
y
)
+
140
(x^2 + 1)(y^2 + 1) + 2(x -y)(1 - xy) = 4(1 + xy) + 140
(
x
2
+
1
)
(
y
2
+
1
)
+
2
(
x
−
y
)
(
1
−
x
y
)
=
4
(
1
+
x
y
)
+
140
.
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