Difference between revisions of "2006 Alabama ARML TST Problems/Problem 5"
(New page: ==Problem== There exist positive integers <math>A</math>, <math>B</math>, <math>C</math>, and <math>D</math> with no common factor greater than 1, such that <center><math>A\log_{1200} 2+B...) |
(No difference)
|
Revision as of 11:58, 17 April 2008
Problem
There exist positive integers , , , and with no common factor greater than 1, such that
Find .
Solution
Simplifying and taking the logarithms away,
Therefore, , , and . Since and are relatively prime, , , , .