1957 AHSME Problems/Problem 42
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Problem 42
If , where and is an integer, then the total number of possible distinct values for is:
Solution
We first use the fact that . Note that and , so and have are periodic with periods at most 4. Therefore, it suffices to check for .
For , we have .
For , we have .
For , we have .
For , we have .
Hence, the answer is .