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The reciprocity theorem for x^8=q (mod p).

If p and q are distinct odd primes, then the quadratic reciprocity theorem states that the congruences x^2=q (mod p) x^2=p (mod q) (1) are both solvable or both unsolvable ...

There are so many theorems due to Fermat that the term "Fermat's theorem" is best avoided unless augmented by a description of which theorem of Fermat is under discussion. ...

Let z be defined as a function of w in terms of a parameter alpha by z=w+alphaphi(z). (1) Then Lagrange's inversion theorem, also called a Lagrange expansion, states that any ...

R^n is homeomorphic to R^m iff n=m. This theorem was first proved by Brouwer.

The two-dimensional version of the ham sandwich theorem.

The Diophantine equation x^2+y^2=p can be solved for p a prime iff p=1 (mod 4) or p=2. The representation is unique except for changes of sign or rearrangements of x and y. ...

If J is a simple closed curve in R^2, the closure of one of the components of R^2-J is homeomorphic with the unit 2-ball. This theorem may be proved using the Riemann mapping ...

The bicommutant theorem is a theorem within the field of functional analysis regarding certain topological properties of function algebras. The theorem says that, given a ...

There are several theorems known as the "sandwich theorem." In calculus, the squeeze theorem is also sometimes known as the sandwich theorem. In graph theory, the sandwich ...