olymmath

AIME 2006a Problem 9

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The sequence a1,a2,…a_1, a_2, \ldots is geometric with a1=aa_1=a and common ratio r,r, where aa and rr are positive integers. Given that log⁡8a1+log⁡8a2+⋯+log⁡8a12=2006,\log_8 a_1+\log_8 a_2+\cdots+\log_8 a_{12} = 2006, find the number of possible ordered pairs (a,r).(a,r).

Dataset text AIME 1983 to 2026. Quoted with source.

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