Difference between revisions of "1985 AHSME Problems/Problem 26"
(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...") |
|||
| Line 17: | Line 17: | ||
==See Also== | ==See Also== | ||
{{AHSME box|year=1985|num-b=25|num-a=27}} | {{AHSME box|year=1985|num-b=25|num-a=27}} | ||
| + | {{MAA Notice}} | ||
Revision as of 12:02, 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 | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
