2006 AIME I Problem 9

The sequence a_1, a_2, \ldots is geometric with a_1=a and common ratio r, where a and r are positive integers. Given that \log_8 a_1+\log_8 a_2+\cdots+\log_8 a_{12} = 2006, find the number of possible ordered pairs (a,r).

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.