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.


C EULER SUM OF POWERS CONJECTURE - FORTRAN IV
C FIND I1,I2,I3,I4,I5 : I1**5+I2**5+I3**5+I4**5=I5**5
      INTEGER I,P5(250),SUMX
      MAXN=250
      DO 1 I=1,MAXN
   1  P5(I)=I**5
      DO 6 I1=1,MAXN
      DO 6 I2=1,MAXN
      DO 6 I3=1,MAXN
      DO 6 I4=1,MAXN	  
      SUMX=P5(I1)+P5(I2)+P5(I3)+P5(I4)
      I5=1
   2  IF(I5-MAXN) 3,3,6
   3  IF(P5(I5)-SUMX) 5,4,6
   4  WRITE(*,300) I1,I2,I3,I4,I5
      STOP
   5  I5=I5+1
      GOTO 2
   6  CONTINUE
 300  FORMAT(5(1X,I3))
      END 