Putnam 2015/ A3

Mathematical Competitions
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Tolaso J Kos
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Putnam 2015/ A3

#1

Post by Tolaso J Kos »

Compute:

\[\log_2\left(\prod_{a=1}^{2015}\prod_{b=1}^{2015}\left(1+e^{2\pi iab/2015}\right)\right)\]
Answer
$13725$
In my opinion, probably the most beautiful question in the competition.
Imagination is much more important than knowledge.
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