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.


extension BinaryInteger {
  @inlinable
  public func power(_ n: Self) -> Self {
    return stride(from: 0, to: n, by: 1).lazy.map({_ in self }).reduce(1, *)
  }
}
 
func sumOfPowers(maxN: Int = 250) -> (Int, Int, Int, Int, Int) {
  let pow5 = (0..<maxN).map({ $0.power(5) })
  let pow5ToN = {n in pow5.firstIndex(of: n)}
 
  for x0 in 1..<maxN {
    for x1 in 1..<x0 {
      for x2 in 1..<x1 {
        for x3 in 1..<x2 {
          let powSum = pow5[x0] + pow5[x1] + pow5[x2] + pow5[x3]
 
          if let idx = pow5ToN(powSum) {
            return (x0, x1, x2, x3, idx)
          }
        }
      }
    }
  }
 
  fatalError("Did not find solution")
}
 
let (x0, x1, x2, x3, y) = sumOfPowers()
 
print("\(x0)^5 + \(x1)^5 + \(x2)^5 \(x3)^5 = \(y)^5")