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:

(off P)
(off S)

(for I 250
   (idx
      'P
      (list (setq @@ (** I 5)) I)
      T )
   (for (J I (>= 250 J) (inc J))
      (idx
         'S
         (list (+ @@ (** J 5)) (list I J))
         T ) ) )
(println
   (catch 'found
      (for A (idx 'P)
         (for B (idx 'S)
            (T (<= (car A) (car B)))
            (and
               (lup S (- (car A) (car B)))
               (throw 'found
                  (conc
                     (cadr (lup S (car B)))
                     (cadr (lup S (- (car A) (car B))))
                     (cdr (lup P (car A))) ) ) ) ) ) ) )