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.


func real Pow5(N);
int  N;
real X, P;
[X:= float(N);
P:= X*X;
P:= P*P;
return P*X;
];
 
int  X0, X1, X2, X3, Y;
real SP;
[for X0:= 1 to 250 do
  for X1:= 1 to X0-1 do
    for X2:= 1 to X1-1 do
      for X3:= 1 to X2-1 do
        [SP:= Pow5(X0) + Pow5(X1) + Pow5(X2) + Pow5(X3);
        for Y:= X0+1 to 250 do
          if Pow5(Y) = SP then
                [IntOut(0, X0);  Text(0, "^^5 + ");
                 IntOut(0, X1);  Text(0, "^^5 + ");
                 IntOut(0, X2);  Text(0, "^^5 + ");
                 IntOut(0, X3);  Text(0, "^^5 = ");
                 IntOut(0, Y);   Text(0, "^^5^m^j");
                 exit;
                ];
        ];
]