The Waring conjecture - actually a problem associated with a number of conjectures, many now being solved - is one of the most fascinating mathematical problems. This article covers new aspects of this problem, with a generalization and new conjectures, some with a tentative solution, and a new framework to tackle the problem. Yet it is written in simple English and accessible to the layman.
I also review a number of famous related mathematical conjectures, including one with a $1 million award still waiting for a solution, as well as Goldbach's conjecture, yet unproved as of today. Many curious properties of the Floor function are also listed, and the emphasis is on machine learning and efficient computer-intensive algorithms to try to find surprising results, which then need to be formally proved or disproved.
Content of this article:
1. General Framework
- Spectacular Result
- New Generalization of Golbach's Conjecture
- New Generalization of Fermat's Conjecture
2. Generalized Waring Problem
- Main Results
- Open Problems
- Fun Facts (Actually, Conjectures!)
3. Algorithms and Source Code
- Case n = 2: Sums of Two Terms
- Case n = 4: Sums of Four Terms
4. Related Conjectures and Solved Problems
- The One Million Dollar Conjecture
Read the full article here.