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.


const MAX_N : u64 = 250;
 
fn eulers_sum_of_powers() -> (usize, usize, usize, usize, usize) {
    let pow5: Vec<u64> = (0..MAX_N).map(|i| i.pow(5)).collect();
    let pow5_to_n = |pow| pow5.binary_search(&pow);
 
    for x0 in 1..MAX_N as usize {
        for x1 in 1..x0 {
            for x2 in 1..x1 {
                for x3 in 1..x2 {
                    let pow_sum = pow5[x0] + pow5[x1] + pow5[x2] + pow5[x3];
                    if let Ok(n) = pow5_to_n(pow_sum) {
                        return (x0, x1, x2, x3, n)
                    }
                }
            }
        }
    }
 
    panic!();
}
 
fn main() {
	let (x0, x1, x2, x3, y) = eulers_sum_of_powers();
	println!("{}^5 + {}^5 + {}^5 + {}^5 == {}^5", x0, x1, x2, x3, y)
}