Difference between revisions of "Mock AIME 4 2006-2007 Problems/Problem 9"
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==Problem== | ==Problem== | ||
| − | Compute the smallest [[positive integer]] <math>k</math> such that the [[fraction]] <center><p><math>\frac{7k+100}{5k-3}</math></p></center> is [[reducible]]. | + | Compute the smallest [[positive integer]] <math>k</math> such that the [[fraction]] <center><p><math>\frac{7k+100}{5k-3}</math></p></center> is [[reducible fraction | reducible]]. |
==Solution== | ==Solution== | ||
Latest revision as of 19:58, 12 February 2007
Problem
Compute the smallest positive integer 
such that the fraction
is reducible.
Solution
Suppose 
is a common divisor of 
and 
. Then 
also divides 
for integers 
. Putting 
and 
gives 
. Since 
is prime and , we have 
. Thus divides , or 
or 
. Since we are looking for the smallest positive solution, our answer is 
.
