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Fifth Term Settlement (Posted on 2012-03-14) Difficulty: 2 of 5
Consider a sequence {a(n)} with a(1) = 2 and a(n) = (a(n-1))2/a(n-2) for all n ≥ 3.

It is known that a(2) and a(5) are positive integers and a(5) ≤ 2012.

What are the possible values of a(5)?

No Solution Yet Submitted by K Sengupta    
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Solution 5 possible values Comment 2 of 2 |

1.The recursion formula implies even integers only.

2. The 2012 limit causes the candidates  for a(2) not to exceed 10.

3. Therefore there are 5 solutions i.e. (a(2),a(5))= ((2,2),(4,32),(6,162),(8,512),(10,1250)).

4. Interesting fact : if a(2)=2   than all members are equal to 2, since
each of the members is 2^2/2.

 


  Posted by Ady TZIDON on 2012-03-14 16:55:52
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