1985 AHSME Problems/Problem 26
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Problem
Find the least positive integer for which is a non-zero reducible fraction.
Solution
For the fraction to be reducible, the greatest common factor of the numerator and the denominator must be greater than . Using the Euclidean algorithm, we compute Since is prime, it follows that this GCD will be unless is a multiple of , which first occurs when , so the answer is .
See Also
1985 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 25 |
Followed by Problem 27 | |
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