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:

   require 'stats'
   (#~ (= <.)@((+/"1)&.:(^&5)))1+4 comb 248
27 84 110 133


1+4 comb 248


(#~ (= <.)@((+/"1)&.:(^&5)))


find5=:3 :0
  y=. 250
  n=. i.y
  p=. n^5
  a=. (#~ 0&<),-/~p
  s=. /:~a
  l=. (i.*:y)(#~ 0&<),-/~p
  c=. 3 comb <.5%:(y^5)%4
  t=. +/"1 c{p
  x=. (t e. s)#t
  |.,&<&~./|:(y,y)#:l#~a e. x
)


   find5''
┌─────────────┬───┐
│27 84 110 133│144│
└─────────────┴───┘