1989 AIME Problems/Problem 4

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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1989 AIME Problems/Problem 4

Problem

Solution

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