Difference between revisions of "2002 AIME I Problems/Problem 8"

(Problem)
(Problem)
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(1) <math>a_1,a_2,a_3\cdots</math> is a nondecreasing sequence of positive integers
 
(1) <math>a_1,a_2,a_3\cdots</math> is a nondecreasing sequence of positive integers
 +
 
(2) <math>a_n=a_{n-1}+a_{n-2}</math> for all <math>n>2</math>
 
(2) <math>a_n=a_{n-1}+a_{n-2}</math> for all <math>n>2</math>
 +
 
(3) <math>a_9=k</math>
 
(3) <math>a_9=k</math>
  

Revision as of 16:36, 25 September 2007

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Problem

Find the smallest integer $k$ for which the conditions

(1) $a_1,a_2,a_3\cdots$ is a nondecreasing sequence of positive integers

(2) $a_n=a_{n-1}+a_{n-2}$ for all $n>2$

(3) $a_9=k$

are satisfied by more than one sequence.

Solution

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See also