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22
Purple Comet 2018 HS problem 22
Purple Comet 2018 HS problem 22
Source:
March 19, 2020
number theory
Problem Statement
Positive integers
a
a
a
and
b
b
b
satisfy
a
3
+
32
b
+
2
c
=
2018
a^3 + 32b + 2c = 2018
a
3
+
32
b
+
2
c
=
2018
and
b
3
+
32
a
+
2
c
=
1115
b^3 + 32a + 2c = 1115
b
3
+
32
a
+
2
c
=
1115
. Find
a
2
+
b
2
+
c
2
a^2 + b^2 + c^2
a
2
+
b
2
+
c
2
.
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