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.


findEulerSumOfPowers
to findEulerSumOfPowers
    set MAX_NUMBER to 250
    set possibleValues to 1..MAX_NUMBER
    set possible5thPowers to each item of possibleValues to the power of 5
    repeat for x0 in 1..250
        repeat for x1 in 1..x0
            repeat for x2 in 1..x1
                repeat for x3 in 1..x2
                    set possibleSum to item x0 of possible5thPowers \
                            plus item x1 of possible5thPowers \
                            plus item x2 of possible5thPowers \
                            plus item x3 of possible5thPowers
                    if possibleSum is in possible5thPowers
                        put x0 & "^5 + " & x1 & "^5 + " & x2 & "^5 + " & x3 & "^5 = " & the item number of possibleSum within possible5thPowers & "^5"
                        return
                    end if
                end repeat
            end repeat
        end repeat
    end repeat
end findEulerSumOfPowers