Definition

Fermat's Last Theorem (FLT)

Part of the Computing fundamentals glossary:

Fermat's Last Theorem (FLT), a significant hypothesis in number theory , was first stated by Pierre de Fermat, a 17th-Century laywer and amateur mathematician. The proposition was discovered by his son Samuel while collecting and organizing the elder Fermat's papers and letters posthumously.

The proposition is as follows. Suppose we have the following equation:

x n + y n = z n

where x , y , and z are nonzero integer s. Then the equation has no solution for integers n larger than 2.

Fermat did not state a proof of this hypothesis, although he said that he had found a remarkable demonstration but did not have space in the margin of his text to write it down. Mathematicians immediately began seeking a proof. (Many mathematicians today doubt that Fermat had actually found a valid proof.) The hypothesis was demonstrated true for increasingly large values of n , but proving the theorem in general, for all integers n greater than 2, remained elusive for centuries. Over the next three hundred years, mathematicians from all over the world sought to prove Fermat's Last Theorem; it was considered by many to be the Holy Grail of mathematics.

Two strategies of proof can reasonably be tried. First, one can assume that the equation has a solution for some nonzero integers x , y , and z , and for some n greater than 2, and then derive a contradiction from this assumption. This tactic is formally known as reductio ad absurdum. Second, one might prove that the equation has no solution for n = 3, and then demonstrate that if the equation has no solution for n = k , where k is an unspecified integer, then there exists no solution for n = k + 1. This is the technique of mathematical induction.

In the 1990s, the British mathematician Andrew Wiles produced a proof of FLT that, after some refinements, has withstood all challenges to date.

This was last updated in March 2011
Posted by: Margaret Rouse

Related Terms

Definitions

  • disruptive technology

    - A disruptive technology is one that displaces an established technology and shakes up the industry. Harvard Business School professor Clayton M. Christensen coined the term.  In his 1997 best-sell... (WhatIs.com)

  • application program interface (API)

    - An application program interface (API) is code that allows two software programs to communicate with each other. Typically, APIs are released for third-party development as part of a software devel... (SearchExchange.com)

  • Microsoft Windows Control Panel

    - The Microsoft Windows Control Panel is a management tool for the Windows operating system (OS) that allows end users to change settings and manage tasks within the OS.  (SearchWindowsServer.com)

Glossaries

  • Computing fundamentals

    - Terms related to computer fundamentals, including computer hardware definitions and words and phrases about software, operating systems, peripherals and troubleshooting.

  • Internet applications

    - This WhatIs.com glossary contains terms related to Internet applications, including definitions about Software as a Service (SaaS) delivery models and words and phrases about web sites, e-commerce ...

Ask a Question About Fermat's Last Theorem (FLT)Powered by ITKnowledgeExchange.com

Get answers from your peers on your most technical challenges

Tech TalkComment

Share
Comments

    Results

    Contribute to the conversation

    All fields are required. Comments will appear at the bottom of the article.