2017 AIME I Problems/Problem 3

Revision as of 16:37, 8 March 2017 by Makorn (talk | contribs) (Created page with "We see that <math>d(n)</math> appears in cycles of <math>20</math>, adding a total of <math>70</math> each cycle. Since <math>\lfloor\frac{2017}{20}\rfloor=100</math>, we know...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

We see that $d(n)$ appears in cycles of $20$, adding a total of $70$ each cycle. Since $\lfloor\frac{2017}{20}\rfloor=100$, we know that by $2017$, there have been $100$ cycles, or $7000$ has been added. This can be discarded, as we're just looking for the last three digits. Adding up the first $17$ of the cycle of $20$, we get that the answer is $\boxed{069}$.

Invalid username
Login to AoPS