Exhaustive search to find the solution for `i^5 + j^5 + k^5 + l^5 = z^5`, known as Euler's conjecture.

euler_conjecture_disprover.py

#!/usr/bin/env python3

#Exhaustive search to find the solution for `i^5 + j^5 + k^5 + l^5 = z^5`, known as Euler's conjecture.
#According to |https://www.math.uci.edu/~brusso/stewart230-231.pdf|, one of the solution is first found in 1966 by exhaustive search.
#Complexity (real, M1 mac): 2.57e-07 * n^3

import math
import sys
import time

n: int = 0

while (True):
    
    start: int = time.time()

    n += 1
    print(n, end = ' ')

    for i in range(1, n + 1):
        for j in range(i, n + 1):
            for k in range(j, n + 1):

                l: int = n

                r: int = i**5 + j**5 + k**5 + l**5

                p: int = math.floor(r**(1 / 5))
                q: int = math.ceil(r**(1 / 5))

                if ((p**5 == r) or (q**5 == r)):
                    if (q**5 == r):
                        p = q
                    print(f'[Solved! {i}^5 + {j}^5 + {k}^5 + {l}^5 = {p}^5]')
                    sys.exit(0)

    print(time.time() - start)