2006 Alabama ARML TST Problems/Problem 5
Problem
There exist positive integers ,
,
, and
with no common factor greater than 1, such that
![$A\log_{1200} 2+B\log_{1200} 3+C\log_{1200} 5=D.$](http://latex.artofproblemsolving.com/a/6/d/a6da2ed10da3db30008df596117c45ab02327603.png)
Find .
Solution
Simplifying and taking the logarithms away,
Therefore, ,
, and
. Since
and
are relatively prime,
,
,
,
.