Fermat's Last Theorem

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Fermat's last theorem

[fer′mäz ¦last ′thir·əm]
The proposition, proven in 1995, that there are no positive integer solutions of the equation x n + y n = z n for n ≥ 3.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

Fermat’s Last Theorem


(or Fermat’s great theorem), the assertion of P. Fermat that the Diophantine equation xn + yn = zn, where n is an integer greater than 2, has no solution in positive integers. The theorem has been proved for a number of values of n, but no proof has been given for the general case.

Despite the simplicity of the formulation of Fermat’s last theorem, its complete proof apparently requires the development of new and profound methods in the theory of Diophantine equations. An unhealthy interest in the proof of the theorem among nonspecialists in mathematics was stimulated at one time by a large international prize, which was withdrawn at the end of World War I.


Dickson, L. E. History of the Theory of Numbers, vols. 1–3. New York, 1934.
Landau, E. Aus der algebraischen Zahlentheorie und über die Fermatsche Vermutung. (Vorlesungen über Zahlentheorie, vol. 3.) Leipzig, 1927.
The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.
References in periodicals archive ?
Obviously, Fermat's Last Theorem is equivalent to the assertion that such a computer program can never halt.
In 1993, Andrew Wiles of Princeton University announced another proof of Fermat's Last Theorem, and for a while it held the ring of truth.
Included are questions that were only recently solved, such as Fermat's Last Theorem and the computer proof of the Four-Color Theorem, as well as unsolved problems such as the Riemann Hypothesis.
Though I was grateful to the folks at MIT, Michigan State, and Stanford for doing all the statistical legwork, they didn't exactly solve Fermat's Last Theorem or uncrypt the Holy Grail.
Mathematicians performed prodigies of mental gymnastics in quest of the proof, until at Cambridge University in 1993, Professor Andrew Wiles, an English academic at Princeton, ended a brilliant course of lectures at the Newton Institute for Mathematical Sciences with his proof of Fermat's Last Theorem and said, `I think I'll stop here.' The distinguished audience, which had been expecting something of the sort, burst into applause and the press announced the discovery to the world.
If Stephen Sondheim can write a musical about Georges Seurat's pointillism, why shouldn't Joshua Rosenblum and Joanne Sydney Lessner write one about Pierre de Fermat's last theorem? Well, because they're not Sondheim.
For example, the recent proof of Fermat's Last Theorem is a striking case of a powerfully enlightening proof and a wholly unenlightening theorem.
This has become known as Fermat's last theorem and although it seems simple enough, the proof long evaded the greatest mathematical minds.
Denyer asks why I do not infer that 1 = 0 from the fact that m + 1 = m (= m + 0), by subtracting m from both sides; or claim that Fermat's Last Theorem is false since [m.sup.m] + [m.sup.m] = [m.sup.m].
Fermat's Last Theorem is the most famous unsolved problem in mathematics.
The most famour unsolved problem in all of mathematics is Fermat's Last Theorem which states that the equation [A.sup.n] + [B.sup.n] = [C.sup.n] has no solution in positive integers A, B, C for n > 2.
Saito begins with a rough outline of his proof of what has become known as Fermat's Last Theorem, then works through it in detail.