Counterexample to Euler's conjecture on sums of powers

euler-conjecture.py

"""
In 1769, Euler conjectured that it was impossible to express an nth power as the sum of fewer than
n nth powers of positive integers. For example, the sum of two cubes is not a cube, the sum of three
fourth powers is not a fourth power, and so on.

In 1966, L. J. Lander and T. R. Parkin found a counterexample: 27^5 + 84^5 + 110^5 + 133^5 = 144^5.
They performed a computer search using a CDC 6600. This was a massive computation for its time, but
it's easy for modern computers.

The following Python script searches for positive integer solutions to a^5 + b^5 + c^5 + d^5 = e^5
where a, b, c, d are less than 200. It should run in under a minute.
"""

from itertools import combinations_with_replacement

for a, b, c, d in combinations_with_replacement(range(1, 200), 4):
    s = (a ** 5) + (b ** 5) + (c ** 5) + (d ** 5)
    e = round(s ** 0.2)
    if e ** 5 == s:
        print(f"{a}^5 + {b}^5 + {c}^5 + {d}^5 = {e}^5")