Difference between revisions of "2024 AMC 12B Problems/Problem 14"
| Line 2: | Line 2: | ||
1. If x is not a multiple of 5: | 1. If x is not a multiple of 5: | ||
| − | we get x^100 \equiv 1 (mod 125) | + | we get x^100\equiv 1 (mod 125) |
2. If x is a multiple of 125: | 2. If x is a multiple of 125: | ||
Revision as of 01:13, 14 November 2024
We split the cases into:
1. If x is not a multiple of 5: we get x^100\equiv 1 (mod 125)
2. If x is a multiple of 125: Clearly the only remainder provides 0
Therefore, the remainders can only be 1 and 0, which gives the answer (B)2
~mitsuihisashi14
