2005 AMC 12A Problems/Problem 21
Problem
How many ordered triples of integers , with , , and , satisfy both and ?
Solution
Casework upon :
- : Then . Thus we get .
- : Then . Thus we get .
- : Then the exponent of becomes huge, and since there is no way we can satisfy the second condition. Hence we have two ordered triples .
See also
2005 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 20 |
Followed by Problem 22 |
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All AMC 12 Problems and Solutions |
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