2006 AIME I Problems/Problem 9: Difference between revisions
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== Problem == | == Problem == | ||
The sequence <math> a_1, a_2, \ldots </math> is geometric with <math> a_1=a </math> and common ratio <math> r, </math> where <math> a </math> and <math> r </math> are positive integers. Given that <math> \log_8 a_1+\log_8 a_2+\cdots+\log_8 a_{12} = 2006, </math> find the number of possible ordered pairs <math> (a,r). </math> | The sequence <math> a_1, a_2, \ldots </math> is geometric with <math> a_1=a </math> and common ratio <math> r, </math> where <math> a </math> and <math> r </math> are positive integers. Given that <math> \log_8 a_1+\log_8 a_2+\cdots+\log_8 a_{12} = 2006, </math> find the number of possible ordered pairs <math> (a,r). </math> | ||
== Solution == | == Solution == | ||
== See also == | == See also == | ||
* [[2006 AIME I]] | * [[2006 AIME I Problems]] | ||
Revision as of 11:14, 30 June 2006
Problem
The sequence 
is geometric with 
and common ratio 
where 
and 
are positive integers. Given that 
find the number of possible ordered pairs 
