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Estimate a percentage (Posted on 2016-08-22) Difficulty: 2 of 5
What percentage of the numbers from one to a million can be represented as the sum of a square and a non-negative cube?

No Solution Yet Submitted by Ady TZIDON    
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A simple upperbound | Comment 3 of 6 |
There are only 100 cubes under a million.
Let C be a cube.  [sqrt(1000000-C^3)] is the number of squares you can add and keep the total under a million.
Add up for all C from to to 100 and you get 84545.

This is an upper bound because some numbers are counted twice or more.  For example 9=1^2+2^3=3^2+0^3.

To refine this you'd need to find which numbers can be done in more than one way and subtract.

  Posted by Jer on 2016-08-22 11:06:05
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