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A problem posed by L. Collatz in 1937, also called the 3x+1 mapping, 3n+1 problem, Hasse's algorithm, Kakutani's problem, Syracuse algorithm, Syracuse problem, Thwaites ...

As a consequence of Matiyasevich's refutation of Hilbert's 10th problem, it can be proved that there does not exist a general algorithm for solving a general quartic ...

An Abelian variety is an algebraic group which is a complete algebraic variety. An Abelian variety of dimension 1 is an elliptic curve.

Let f(z) be a transcendental meromorphic function, and let D_1, D_2, ..., D_5 be five simply connected domains in C with disjoint closures (Ahlfors 1932). Then there exists j ...

Given a field F and an extension field K superset= F, an element alpha in K is called algebraic over F if it is a root of some nonzero polynomial with coefficients in F. ...

An algebraic equation in n variables is an polynomial equation of the form f(x_1,x_2,...,x_n)=sum_(e_1,...,e_n)c_(e_1,e_2,...,e_n)x_1^(e_1)x_2^(e_2)...x_n^(e_n)=0, where the ...

An algebraic set is the locus of zeros of a collection of polynomials. For example, the circle is the set of zeros of x^2+y^2-1 and the point at (0,0) is the set of zeros of ...

A Banach algebra A for which H^1(A,X^*)=Z^1(A,X^*)/B^1(A,X^*)=0 for all Banach A-bimodules X is called amenable (or Johnson amenable; Helemskii 1989, 1997). This notion was ...

The Andrews-Schur identity states sum_(k=0)^nq^(k^2+ak)[2n-k+a; k]_q =sum_(k=-infty)^inftyq^(10k^2+(4a-1)k)[2n+2a+2; n-5k]_q([10k+2a+2]_q)/([2n+2a+2]_q) (1) where [n; m]_q is ...

A plane tiling is said to be isohedral if the symmetry group of the tiling acts transitively on the tiles, and n-isohedral if the tiles fall into n orbits under the action of ...