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9 March, 17:56

What is the least possible value of the smallest of 99 consecutive positive integers whose sum is a perfect cube

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  1. 9 March, 19:03
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    First, try 99^3 = 970299; therefore, it is not the least possible value.

    The above number is a multiple of 99, so we can factor this out to find the least possible value. So we try to factor 99:

    99 = 9 * 11

    99 = 3^2 * 11^ 1

    and 3^3 * 11^3 = 35937

    The least possible value is 4^1 + 11^2 = 125. Its sum is 125 which is a perfect cube.
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