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The Heine-Borel theorem states that a subspace of R^n (with the usual topology) is compact iff it is closed and bounded. The Heine-Borel theorem can be proved using the ...

If p is a prime number and a is a natural number, then a^p=a (mod p). (1) Furthermore, if pa (p does not divide a), then there exists some smallest exponent d such that ...

A theorem that guarantees that the trajectory of Langton's ant is unbounded.

Due to Euler's prolific output, there are a great number of theorems that are know by the name "Euler's theorem." A sampling of these are Euler's displacement theorem for ...

A generalization of Turán's theorem to non-complete graphs.

Alexandrov's theorem addresses conditions under which a polygon will fold into a convex polyhedron (Malkevitch).

A theorem which treats constructions of fields of field characteristic p.

A Tauberian theorem is a theorem that deduces the convergence of an series on the basis of the properties of the function it defines and any kind of auxiliary hypothesis ...

Let f(x) be differentiable on the open interval (a,b) and continuous on the closed interval [a,b]. Then there is at least one point c in (a,b) such that ...

If n>19, there exists a Poulet number between n and n^2. The theorem was proved in 1965.