2017 AIME I Problems/Problem 3
Contents
[hide]Problem 3
For a positive integer , let be the units digit of . Find the remainder when is divided by .
Solution
We see that appears in cycles of and the cycles are adding a total of each cycle. Since , we know that by , there have been cycles and has been added. This can be discarded as we're just looking for the last three digits. Adding up the first of the cycle of , we can see that the answer is .
~ Maths_Is_Hard
Video Solution
https://youtu.be/BiiKzctXDJg ~ Shrea S
See Also
2017 AIME I (Problems • Answer Key • Resources) | ||
Preceded by Problem 2 |
Followed by Problem 4 | |
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