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.


 
# syntax: GAWK -f EULERS_SUM_OF_POWERS_CONJECTURE.AWK
BEGIN {
    start_int = systime()
    main()
    printf("%d seconds\n",systime()-start_int)
    exit(0)
}
function main(  sum,s1,x0,x1,x2,x3) {
    for (x0=1; x0<=250; x0++) {
      for (x1=1; x1<=x0; x1++) {
        for (x2=1; x2<=x1; x2++) {
          for (x3=1; x3<=x2; x3++) {
            sum = (x0^5) + (x1^5) + (x2^5) + (x3^5)
            s1 = int(sum ^ 0.2)
            if (sum == s1^5) {
              printf("%d^5 + %d^5 + %d^5 + %d^5 = %d^5\n",x0,x1,x2,x3,s1)
              return
            }
          }
        }
      }
    }
}
 