2021 Fall AMC 10B Problems/Problem 22
Problem
For each integer , let be the sum of all products , where and are integers and . What is the sum of the 10 least values of such that is divisible by ?
Solution 1
To get from to , we add .
Now, we can look at the different values of mod . For and , then we have . However, for , we have
Clearly, Using the above result, we have , and , , and are all divisible by . After , we have , , and all divisible by , as well as , and . Thus, our answer is . -BorealBear
Solution 2 (bash)
See Also
2021 Fall AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 21 |
Followed by Problem 23 | |
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All AMC 10 Problems and Solutions |
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