Difference between revisions of "1989 AIME Problems/Problem 4"

 
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== Problem ==
 
== Problem ==
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If <math>a<b<c<d<e^{}_{}</math> are consecutive positive integers such that <math>b+c+d^{}_{}</math> is a perfect square and <math>a+b+c+d+e^{}_{}</math> is a perfect cube, what is the smallest possible value of <math>c^{}_{}</math>?
  
 
== Solution ==
 
== Solution ==
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{{solution}}
  
 
== See also ==
 
== See also ==
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* [[1989 AIME Problems/Problem 5|Next Problem]]
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* [[1989 AIME Problems/Problem 3|Previous Problem]]
 
* [[1989 AIME Problems]]
 
* [[1989 AIME Problems]]

Revision as of 22:56, 24 February 2007

Problem

If $a<b<c<d<e^{}_{}$ are consecutive positive integers such that $b+c+d^{}_{}$ is a perfect square and $a+b+c+d+e^{}_{}$ is a perfect cube, what is the smallest possible value of $c^{}_{}$?

Solution

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See also

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