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The only whole number solution to the Diophantine equation y^3=x^2+2 is y=3, x=+/-5. This theorem was offered as a problem by Fermat, who suppressed his own proof.

The use of the principle of mathematical induction in a proof. Induction used in mathematics is often called mathematical induction.

An oriented surface for which every point belongs to a Wiedersehen pair. Proof of the Blaschke conjecture established that the only Wiedersehen surfaces are the standard ...

For any positive integer k, there exists a prime arithmetic progression of length k. The proof is an extension of Szemerédi's theorem.

The word "algebra" is a distortion of the Arabic title of a treatise by al-Khwārizmī about algebraic methods. In modern usage, algebra has several meanings. One use of the ...

A "square" word consists of two identical adjacent subwords (for example, acbacb). A squarefree word contains no square words as subwords (for example, abcacbabcb). The only ...

A prize of 100000 German marks offered for the first valid proof of Fermat's last theorem (Ball and Coxeter 1987, p. 72; Barner 1997; Hoffman 1998, pp. 193-194 and 199). The ...

1 uncia=1/(12). The word uncia was Latin for a unit equal to 1/12 of another unit called the as. The words "inch" (1/12 of a foot) and "ounce" (originally 1/12 of a pound and ...

An inequality which implies the correctness of the Robertson conjecture (Milin 1964). de Branges (1985) proved this conjecture, which led to the proof of the full Bieberbach ...

An Eulerian cycle, also called an Eulerian circuit, Euler circuit, Eulerian tour, or Euler tour, is a trail which starts and ends at the same graph vertex. In other words, it ...