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4
SMT 2023 Algebra #4
SMT 2023 Algebra #4
Source:
May 3, 2023
Problem Statement
If the sum of the real roots
x
x
x
to each of the equations
2
2
x
−
2
x
+
1
+
1
−
1
k
2
=
0
2^{2x}-2^{x+1}+1-\frac{1}{k^2}=0
2
2
x
−
2
x
+
1
+
1
−
k
2
1
=
0
for
k
=
2
,
3
,
…
,
2023
k=2,3,\dots,2023
k
=
2
,
3
,
…
,
2023
is
N
N
N
, what is
2
N
2^N
2
N
?
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