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.



Euler's (disproved) sum of powers   conjecture

  At least  k  positive  kth  powers are required to sum to a  kth  power,  
  except for the trivial case of one  kth power:  yk = yk 



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.



Task

Write a program to search for an integer solution for:


  x05 + x15 + x25 + x35 == y5 

Where all     xi's   and    y    are distinct integers between   0   and   250   (exclusive).

Show an answer here.



Related tasks

   Pythagorean quadruples. 
   Pythagorean triples.


pow5s:=[1..249].apply("pow",5); // (1^5, 2^5, 3^5 .. 249^5)
pow5r:=pow5s.enumerate().apply("reverse").toDictionary(); // [144^5:144, ...]
foreach x0,x1,x2,x3 in (249,x0,x1,x2){
   sum:=pow5s[x0] + pow5s[x1] + pow5s[x2] + pow5s[x3];
   if(pow5r.holds(sum))
      println("%d^5 + %d^5 + %d^5 + %d^5 = %d^5"
          .fmt(x3+1,x2+1,x1+1,x0+1,pow5r[sum]+1));
      break(4);  // the foreach is actually four loops
}