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Cubic Consecutive Conundrum (Posted on 2024-12-05)

It is given that 181² can be written as the difference of the cubes of two consecutive positive integers. Find the sum of these two integers.

No Solution Yet Submitted by Danish Ahmed Khan

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using calculus

| Comment 4 of 5 |

The derivative of x^3 = 3x^2

Set this equal to 181^2 and solve for the approximate midpoint of the two integers

3x^2 = 181^2

x = 181/sqrt(3) = 104.5004

so n + (n+1) = 104.5 * 2 = 209

Posted by Steve Herman on 2024-12-06 07:15:15

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