Fermat's Two Page Claim of his Last Problem Verified

Abstract

In the 1650s Fermat claimed a short two-page proof of his last theorem but could not fit it into the margin. This article vindicates Fermat’s claim that has never been verified. The proof of Fermat’s claim has held up for over 360 years. The solution to the problem given in this article shows that the problem can be solved in two pages and clarifies why the problem resisted solution by thousands of mathematicians both professional and amateur. The author solved the problem in 1998 but opted not to publish it until recent years. However, the author featured the proof publicly in his website challenging anyone to find a flaw in the proof. No objections ever occurred. The proof uses only theorems and proof techniques available to Fermat. It is a devious proof that can be understood by a gifted high school student because it only uses theorems taught in high school along with an interesting algorithm devised by the author for the purpose of addressing infinity issues obstructing the finding of a simple two-page solution. The algorithm invented by the author ended the quest to solve the theorem and allows the viewer of the proof to understand why this problem has resisted so many attempts. The author believes this solution is the only one possible. The author Dr. Joseph E. L. Brierly is skeptical about the many-page solution claimed by Sir Andrew Wiles some years ago. Even professional mathematicians avoid attempting to verify pages of subtle reasoning. There is a strong likelihood of errors in proofs of that magnitude. As everyone knows a computer operating system invariably has multiple bugs due to the large number of lines of coding. In essence, there is no reason for an impractical-to-verify solution taking pages of subtle reasoning when there exists an easily reviewed two-page solution given in this research article. There exist few important theorems in mathematics and physics that require more than 5 pages of reasoning.