Difference between revisions of "1998 AIME Problems/Problem 8"

 
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== Problem ==
 
== Problem ==
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Except for the first two terms, each term of the sequence <math>1000, x, 1000 - x,\ldots</math> is obtained by subtracting the preceding term from the one before that.  The last term of the sequence is the first [[negative]] term encounted.  What positive integer <math>x</math> produces a sequence of maximum length?
  
== Solution ==
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Solutions were removed
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__TOC__
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Help why is there no solution
  
 
== See also ==
 
== See also ==
* [[1998 AIME Problems]]
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{{AIME box|year=1998|num-b=7|num-a=9}}
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[[Category:Intermediate Number Theory Problems]]
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{{MAA Notice}}

Revision as of 21:09, 18 October 2024

Problem

Except for the first two terms, each term of the sequence $1000, x, 1000 - x,\ldots$ is obtained by subtracting the preceding term from the one before that. The last term of the sequence is the first negative term encounted. What positive integer $x$ produces a sequence of maximum length?



Solutions were removed

Contents

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Help why is there no solution

See also

1998 AIME (ProblemsAnswer KeyResources)
Preceded by
Problem 7
Followed by
Problem 9
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
All AIME Problems and Solutions

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