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.


fun main(args: Array<String>) {
    val p5 = LongArray(250){ it.toLong() * it * it * it * it }
    var sum: Long
    var y: Int
    var found = false
    loop@ for (x0 in 0 .. 249)
        for (x1 in 0 .. x0 - 1)
            for (x2 in 0 .. x1 - 1)
                for (x3 in 0 .. x2 - 1) {
                    sum = p5[x0] + p5[x1] + p5[x2] + p5[x3]
                    y = p5.binarySearch(sum)
                    if (y >= 0) {
                        println("$x0^5 + $x1^5 + $x2^5 + $x3^5 = $y^5")
                        found = true
                        break@loop
                    }
                }
    if (!found) println("No solution was found")
}