MathDB

Sequence and Logs

Source: 2006 AIME A Problem 9

March 9, 2006

ratiologarithmsmodular arithmeticAMC

Problem Statement

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)

.

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