Prove or disprove that every integer can be expressed as either the sum of 3 cubes, or the sum of 3 cubes + 4.
N=33 was cracked earlier this year.
If you add the cubes of each of 8866128975287528, 8778405442862239 and 2736111468807040 you'll get 33.
N=42 is the only uncracked number < 100.
Here's a general article.
https://www.quantamagazine.org/sumofthreecubesproblemsolvedforstubbornnumber3320190326/
The solver's paper is mostly accessible.
https://people.maths.bris.ac.uk/~maarb/papers/cubesv1.pdf

Posted by xdog
on 20190601 13:02:57 