2017 AIME I Problems/Problem 2
Problem 2
When each of , , and is divided by the positive integer , the remainder is always the positive integer . When each of , , and is divided by the positive integer , the remainder is always the positive integer . Find .
Solution
Let's tackle the first part of the problem first. We can safely assume: Now, if we subtract two values: which also equals Similarly, Since is the only common factor, we can assume that , and through simple division, that .
Using the same method on the second half: Then. The common factor is , so and through division, .
The answer is
~IYN~
See Also
2017 AIME I (Problems • Answer Key • Resources) | ||
Preceded by Problem 1 |
Followed by Problem 3 | |
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