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Purple Comet Problems
2016 Purple Comet Problems
20
Purple Comet 2016 HS Problem 20
Purple Comet 2016 HS Problem 20
Source:
April 12, 2018
Purple Comet
Problem Statement
Positive integers a, b, c, d, and e satisfy the equations
(
a
+
1
)
(
3
b
c
+
1
)
=
d
+
3
e
+
1
(a + 1)(3bc + 1) = d + 3e + 1
(
a
+
1
)
(
3
b
c
+
1
)
=
d
+
3
e
+
1
(
b
+
1
)
(
3
c
a
+
1
)
=
3
d
+
e
+
13
(b + 1)(3ca + 1) = 3d + e + 13
(
b
+
1
)
(
3
c
a
+
1
)
=
3
d
+
e
+
13
(
c
+
1
)
(
3
a
b
+
1
)
=
4
(
26
−
d
−
e
)
−
1
(c + 1)(3ab + 1) = 4(26-d- e) - 1
(
c
+
1
)
(
3
ab
+
1
)
=
4
(
26
−
d
−
e
)
−
1
Find
d
2
+
e
2
d^2+e^2
d
2
+
e
2
.
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