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.


F eulers_sum_of_powers()
   V max_n = 250
   V pow_5 = (0 .< max_n).map(n -> Int64(n) ^ 5)
   V pow5_to_n = Dict(0 .< max_n, n -> (Int64(n) ^ 5, n))
 
   L(x0) 1 .< max_n
      L(x1) 1 .< x0
         L(x2) 1 .< x1
            L(x3) 1 .< x2
               V pow_5_sum = pow_5[x0] + pow_5[x1] + pow_5[x2] + pow_5[x3]
               I pow_5_sum C pow5_to_n
                  V y = pow5_to_n[pow_5_sum]
                  R (x0, x1, x2, x3, y)
 
V r = eulers_sum_of_powers()
print(‘#.^5 + #.^5 + #.^5 + #.^5 = #.^5’.format(r[0], r[1], r[2], r[3], r[4]))