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.


PROGRAM EULERO
 
CONST MAX=250
 
!$DOUBLE
 
FUNCTION POW5(X)
    POW5=X*X*X*X*X
END FUNCTION
 
!$INCLUDE="PC.LIB"
 
BEGIN
   CLS
   FOR X0=1 TO MAX DO
     FOR X1=1 TO X0 DO
        FOR X2=1 TO X1 DO
           FOR X3=1 TO X2 DO
              LOCATE(3,1) PRINT(X0;X1;X2;X3)
              SUM=POW5(X0)+POW5(X1)+POW5(X2)+POW5(X3)
              S1=INT(SUM^0.2#+0.5#)
              IF SUM=POW5(S1) THEN PRINT(X0,X1,X2,X3,S1) END IF
           END FOR
        END FOR
     END FOR
   END FOR
END PROGRAM