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

A theorem proved by É. Cartan in 1913 which classifies the irreducible representations of complex semisimple Lie algebras.

The hinge theorem says that if two triangles DeltaABC and DeltaA^'B^'C^' have congruent sides AB=A^'B^' and AC=A^'C^' and ∠A>∠A^', then BC>B^'C^'.

A theorem which states that if a Kähler form represents an integral cohomology class on a compact manifold, then it must be a projective Abelian variety.

The Kronecker-Weber theorem, sometimes known as the Kronecker-Weber-Hilbert theorem, is one of the earliest known results in class field theory. In layman's terms, the ...

A bounded entire function in the complex plane C is constant. The fundamental theorem of algebra follows as a simple corollary.

Let T be a maximal torus of a group G, then T intersects every conjugacy class of G, i.e., every element g in G is conjugate to a suitable element in T. The theorem is due to ...

If the first case of Fermat's last theorem is false for the prime exponent p, then 3^(p-1)=1 (mod p^2).

A theorem stated in 1882 which cannot be derived from Euclid's postulates. Given points a, b, c, and d on a line, if it is known that the points are ordered as (a,b,c) and ...

Any motion of a rigid body in space at every instant is a screw motion. This theorem was proved by Mozzi and Cauchy.