Fermat's theorem

[′fer‚mäz ‚thir·əm]

(mathematics)

The proposition that, if p is a prime number and a is a positive integer which is not divisible by p, then a ^p-1-1 is divisible by p.

The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

Fermat’s Theorem

(or Fermat’s lesser theorem), a fundamental theorem of number theory. The theorem states that if p is a prime number and a is a whole number not divisible by p, then a^p–1 – 1 is divisible by p—that is, a^p–1 ≡ 1 (mod p). The theorem was set forth by P. Fermat without proof; the first proof was given by L. Euler.

References in periodicals archive

What is happening to Fermat's theorem solved by your dad?

Thank God I once failed all my papers at UNILAG -Chike-Obi

These two lectures are followed by a series of essays on artificial intelligence, Fermat's theorem, Euclid, and Hilbert.

Borges and Mathematics

For example, he describes how Fermat's last theorem, first posited in the year 1630, remained unsolved until Andrew Wiles published his solution in 1995 while also explaining how work on Fermat's theorem led to the development of algebraic number theory and complex analysis.

Visions of infinity; the great mathematical problems

The first chapter is a brilliant insight into the beauty of mathematics--but no teacher of maths needs an introduction to Fermat's Theorem! The heart of the book is the author's case for a new kind of classroom teaching using cooperative problem solving to encourage deep learning rather than the rote learning of processes.

Boaler, Jo: The Elephant in the Classroom: Helping Children Learn and Love Maths

Little Fermat's Theorem: For any integer a and any prime p, we have the congruence

On the Smarandache divisibility theorem

It is about Fermat's theorem, which a young British mathematician, Andrew Wiles, proved over 300 years after Fermat.

Tribute to Sir Arthur C. Clarke before his death in March at age 90, Sir Arthur C. Clarke greeted many visitors from around the world. among them was Venezuelan futurist and transhumanist scholar Jose Cordeiro, who here recounts his meetings with Clarke in Sri Lanka

Fermat's theorem had bedeviled mathematicians for 350 years.

Beaten to the punch

While this sounds good on paper, twitchy, high- strung eggheads rarely project a good leader image, spending as much time as they do pondering Fermat's Theorem, muttering to themselves and collecting their toenail clippings in large jars for future cloning experiments they plan to get to just as soon as they finish calculating Pi to the 20 billionth decimal and cleaning up the garage.

Al Gore: Omega Man?

85) and is expected to have at least two more "branches." Although this volume is considerably more linear than the two previous ones, genres are constantly mixed as autobiographical material is interlaced with erudition (on the history of mathematics), references to contemporary events, theoretical discussions (of Fermat's theorem, for example), essays (on the Field Prize), and vignettes of people Roubaud has known, some of them of importance in mathematics and intellectual history.

Mathematique

Since it will not, like Fermat's theorem, ever submit to proof, the Gogol problem persists as a peculiar challenge to the capacities of literary scholars.

Robert A. Maguire, Exploring Gogol

Quoted in the June Scientific American, veteran mathematician Andre Weil of the Institute for Advanced Study said, "[T]o some extent, proving Fermat's theorem is like climbing Everest.

Last word not yet in on Fermat's conjecture

Just as 300 years of failed efforts to prove the hypothesis of Fermat's theorem did not demonstrate the falsity of that mathematical hypothesis, as has now been seen through its proof in the 1980s, a proof built upon the work of earlier "failures," so the falsity of the "communist hypothesis" has not been demonstrated by the perceived failures of successive self-declared socialist and communist regimes and movements, argues French philosopher Badiou.

The communist hypothesis