Difference between revisions of "1985 AHSME Problems/Problem 26"
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Revision as of 13:02, 5 July 2013
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 . By the Euclidean algorithm,
Since is prime, must be a multiple of , which first occurs when .
See Also
1985 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 25 |
Followed by Problem 27 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 | ||
All AHSME Problems and Solutions |
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