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.


def eulers_sum_of_powers():
    max_n = 250
    pow_5 = [n**5 for n in range(max_n)]
    pow5_to_n = {n**5: n for n in range(max_n)}
    for x0 in range(1, max_n):
        for x1 in range(1, x0):
            for x2 in range(1, x1):
                for x3 in range(1, x2):
                    pow_5_sum = sum(pow_5[i] for i in (x0, x1, x2, x3))
                    if pow_5_sum in pow5_to_n:
                        y = pow5_to_n[pow_5_sum]
                        return (x0, x1, x2, x3, y)
 
print("%i**5 + %i**5 + %i**5 + %i**5 == %i**5" % eulers_sum_of_powers())