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

### See also

Solution for 42

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