Browse Definitions :
Definition

Fermat's Last Theorem (FLT)

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

Continue Reading About Fermat's Last Theorem (FLT)

SearchCompliance
  • OPSEC (operations security)

    OPSEC (operations security) is a security and risk management process and strategy that classifies information, then determines ...

  • smart contract

    A smart contract is a decentralized application that executes business logic in response to events.

  • compliance risk

    Compliance risk is an organization's potential exposure to legal penalties, financial forfeiture and material loss, resulting ...

SearchSecurity
  • biometric verification

    Biometric verification is any means by which a person can be uniquely identified by evaluating one or more distinguishing ...

  • password

    A password is a string of characters used to verify the identity of a user during the authentication process.

  • biometrics

    Biometrics is the measurement and statistical analysis of people's unique physical and behavioral characteristics.

SearchHealthIT
SearchDisasterRecovery
  • What is risk mitigation?

    Risk mitigation is a strategy to prepare for and lessen the effects of threats faced by a business.

  • change control

    Change control is a systematic approach to managing all changes made to a product or system.

  • disaster recovery (DR)

    Disaster recovery (DR) is an organization's ability to respond to and recover from an event that affects business operations.

SearchStorage
  • PCIe SSD (PCIe solid-state drive)

    A PCIe SSD (PCIe solid-state drive) is a high-speed expansion card that attaches a computer to its peripherals.

  • VRAM (video RAM)

    VRAM (video RAM) refers to any type of random access memory (RAM) specifically used to store image data for a computer display.

  • virtual memory

    Virtual memory is a memory management technique where secondary memory can be used as if it were a part of the main memory.

Close