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2021 CMIMC
2.6 1.3
2021 Alg/NT Div 1 P3 (Div 2 P6)
2021 Alg/NT Div 1 P3 (Div 2 P6)
Source:
March 2, 2021
algebra
Problem Statement
Let
a
a
a
and
b
b
b
be complex numbers such that
(
a
+
1
)
(
b
+
1
)
=
2
(a+1)(b+1)=2
(
a
+
1
)
(
b
+
1
)
=
2
and
(
a
2
+
1
)
(
b
2
+
1
)
=
32.
(a^2+1)(b^2+1)=32.
(
a
2
+
1
)
(
b
2
+
1
)
=
32.
Compute the sum of all possible values of
(
a
4
+
1
)
(
b
4
+
1
)
.
(a^4+1)(b^4+1).
(
a
4
+
1
)
(
b
4
+
1
)
.
Proposed by Kyle Lee
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