1985 AHSME Problems/Problem 26
Revision as of 00:13, 29 October 2011 by Admin25 (talk | contribs) (Created page with "==Problem== Find the least positive integer <math> n </math> for which <math> \frac{n-13}{5n+6} </math> is a non-zero reducible fraction. <math> \mathrm{(A)\ } 45 \qquad \ma...")
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 |