  links to this page:    Very first steps in a Workspace window Sum of three cubes: 42 LargePositiveInteger LargeNegativeInteger         Diophantine equation example
Last updated at 10:29 pm UTC on 5 January 2022
A Diophantine equation is a polynomial equation, usually involving two or more unknowns, such that the only solutions of interest are the integer ones
(https://en.wikipedia.org/wiki/Diophantine_equation).

https://en.wikipedia.org/wiki/Sums_of_three_cubes

Very nice video introducing the problem .

The solution for 33 was discovered by Andrew R. Booker in 2019.
https://people.maths.bris.ac.uk/~maarb/papers/cubesv1.pdf

### Numerical checking the solution for 33

``` | x y z |
x := 8866128975287528.
y := -8778405442862239.
z := -2736111468807040.```
"is the first solution of"
` (x ** 3) + (y ** 3) + (z ** 3) = 33 `
" evaluating this with Squeak gives the result"
` true`

``` x ** 3
8866128975287528 * 8866128975287528 * 8866128975287528
696950821015779435648178972565490929714876221952```

` 696950821015779435648178972565490929714876221952 class LargePositiveInteger`