Problem Statement

There is a conjecture in mathematics that held for over two hundred years before it was disproved by the finding of a counterexample in 1966 by Lander and Parkin. This conjecture is called Euler's sum of powers conjecture and can be stated as such: In 1966, Leon J. Lander and Thomas R. Parkin used a brute-force search on a CDC 6600 computer restricting numbers to those less than 250. The task consists in writing a program to search for an integer solution of

x

0

5

x

1

5

x

2

5

x

3

5

=

y

5

{\displaystyle x_{0}^{5}+x_{1}^{5}+x_{2}^{5}+x_{3}^{5}=y^{5}}

where all

x

i

{\displaystyle x_{i}}

and

y

{\displaystyle y}

are distinct integers between 0 and 250 (exclusive). Show an answer here. Related tasks are:

Let's start with the solution:

: eulerSum
| i j k l ip jp kp |
   250 loop: i [
      i 5 pow ->ip
      i 1 + 250 for: j [
         j 5 pow ip + ->jp
         j 1 + 250 for: k [
            k 5 pow jp + ->kp
            k 1 + 250 for: l [
               kp l 5 pow + 0.2 powf dup asInteger == ifTrue: [ [ i, j, k, l ] println ]
              ]
            ]
         ]
      ] ;