four_fifths

four_fifths, a MATLAB 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.

Licensing:

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

Languages:

four_fifths is available in a MATLAB version, and a Python version.

Related Data and codes:

four_fifths_test

subset, a MATLAB 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.

Reference:

1. Brian Hayes,
   Four Fifths = A Fifth,
   https://bit-player.org/2014/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:

• four_fifths.m, the source code.
• vector_sumlex_next.m, returns the next vector, in order of sum, with vectors of equal sum ordered lexicographically;