four_fifths, a Python code which searches for a solution to the problem of finding four fifth powers that sum to a fifth power, that is, integers a, b, c, d and e such that a^5+b^5+c^5+d^5=e^5. Euler conjectured that no solution was possible. The code is by Brian Hayes.


The computer code and data files described and made available on this web page are distributed under the MIT license


four_fifths is available in a Python version.

Related Data and codes:

subset, a Python code which enumerates, generates, randomizes, ranks and unranks combinatorial objects including combinations, compositions, Gray codes, index sets, partitions, permutations, polynomials, subsets, and Young tables. Backtracking routines are included to solve some combinatorial problems.


Brian Hayes


  1. Brian Hayes,
    Four Fifths = A Fifth,,
    posted 03 December 2014.
  2. L J Lander, T R Parkin,
    Counterexample to Euler's conjecture on sums of like powers,
    Bulletin of the American Mathematical Society,
    Volume 72, Number 6, page 1079, November 1966.

Source Code:

Last revised on 21 October 2019.