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.
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|
|-O1 (-O)||3m 59.017s|
So, use -Ofast or -O3 unless you have time to kill.