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Putnam 2020 B1

Source: 81st William Lowell Putnam Competition

February 22, 2021
Putnamabstract algebraPutnam 2020

Problem Statement

For a positive integer nn, define d(n)d(n) to be the sum of the digits of nn when written in binary (for example, d(13)=1+1+0+1=3d(13)=1+1+0+1=3). Let S=∑k=12020(−1)d(k)k3. S=\sum_{k=1}^{2020}(-1)^{d(k)}k^3. Determine SS modulo 20202020.
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