# Fermat's Last Theorem

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## Fermat's last theorem

[fer′mäz ¦last ′thir·əm] (mathematics)

The proposition, proven in 1995, that there are no positive integer solutions of the equation

*x*^{ n }+*y*^{ n }=*z*^{ n }for*n*≥ 3.## Fermat’s Last Theorem

(or Fermat’s great theorem), the assertion of P. Fermat that the Diophantine equation *x ^{n}* +

*y*=

^{n}*z*, where

^{n}*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of the theorem among nonspecialists in mathematics was stimulated at one time by a large international prize, which was withdrawn at the end of World War I.

### REFERENCES

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.