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Putnam
2015 Putnam
A3
A3
Part of
2015 Putnam
Problems
(1)
Putnam 2015 A3
Source:
12/6/2015
Compute
log
2
(
∏
a
=
1
2015
∏
b
=
1
2015
(
1
+
e
2
π
i
a
b
/
2015
)
)
\log_2\left(\prod_{a=1}^{2015}\prod_{b=1}^{2015}\left(1+e^{2\pi iab/2015}\right)\right)
lo
g
2
(
a
=
1
∏
2015
b
=
1
∏
2015
(
1
+
e
2
πiab
/2015
)
)
Here
i
i
i
is the imaginary unit (that is,
i
2
=
−
1
i^2=-1
i
2
=
−
1
).
Putnam
Putnam 2015
Putnam number theory
roots of unity