2001 AIME II Problems/Problem 10
Problem
How many positive integer multiples of 1001 can be expressed in the form , where and are integers and ?
Solution
Factoring . We have . This means that . By Euler's totient theorem, . If , then we can have solutions of . If , we can have the solutions of . Likewise, we have .
See also
2001 AIME II (Problems • Answer Key • Resources) | ||
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Followed by Problem 11 | |
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