What percentage of the numbers from one to a million can be represented as the sum of a square and a non-negative cube?
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