Determine the number of ordered pairs (a, b) of integers such that \log _{a} b+ 6 \log _{b} a=5,2 \leq a \leq 2005, and 2 \leq b \leq 2005.
Determine the number of ordered pairs (a, b) of integers such that \log _{a} b+ 6 \log _{b} a=5,2 \leq a \leq 2005, and 2 \leq b \leq 2005.