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Cubic Minimum (Posted on 2014-09-26) Difficulty: 3 of 5
S is the minimum positive integer whose cube root is of the form T + U, where T is a positive integer and U is a positive real number less than 0.00001.

Determine the value of S.

No Solution Yet Submitted by K Sengupta    
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generalised approach. | Comment 5 of 7 |

Let S be a qualifying number {2,6,19,58,183...}.

Then some integer [S*10^(1/2) +/- 10^(1/2)] is the next qualifying number:

578.6968118 = 578, 1827.796488 = 1826, 5774.319007 = 5774, etc.

It's not exact but it does mean there are never more than a few numbers to check, which can be helpful once the solutions get beyond 9 or 10 digits.

Edited on September 27, 2014, 2:20 am
  Posted by broll on 2014-09-27 01:09:51

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