# Unsolved inequality

The following inequality resulted from Waring's problem. Paraphrased from Wikipedia:

Are there any positive integers

k≥ 6 such that:Mahler proved that there could only be a finite number of

k; none are known.

Kubina and Wunderlich, in their book *Extending
Waring's conjecture to 471,600,000*, have shown that any such
`k` would need be larger than 471,600,000.

It is conjectured, but not proven, that no such `k` exist. I have
been unable to find a name for this specific inequality. From what I have found,
it is not called "Waring's problem" but instead is a result of Waring's
problem.

## Unsolved-inequality.cpp

Change the value of `PRECISION`

to increase the maximum
`k` (or more accurately the maximum that the program can reach. You can also change the
starting `k` by changing the value of `k = 6`

below the
beginning of the main function. This program is not optimized, and there are
definitely better ways to brute-force this inequality.

This program was tested using the g++ compiler. I recommend using -Ofast. Below is a comparison of run times until precision is exceeded using the different optimization flags. While my system will be different from others, the relative time improvements are what is important.

Optimization Flag | Real Time |
---|---|

None | 11m 40.775s |

-O1 (-O) | 3m 59.017s |

-O2 | 2m 47.888s |

-O3 | 1m 50.419s |

-Ofast | 1m 47.860s |

So, use -Ofast or -O3 unless you have time to kill.