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Bézout's theorem for curves states that, in general, two algebraic curves of degrees m and n intersect in m·n points and cannot meet in more than m·n points unless they have ...

Given a triangle with polygon vertices A, B, and C and points along the sides D, E, and F, a necessary and sufficient condition for the cevians AD, BE, and CF to be ...

A reduction system is called confluent (or globally confluent) if, for all x, u, and w such that x->_*u and x->_*w, there exists a z such that u->_*z and w->_*z. A reduction ...

A differential-algebraic equation (DAE) is a type of differential equation in which the derivatives are not (in general) expressed explicitly, and typically derivatives of ...

A field is any set of elements that satisfies the field axioms for both addition and multiplication and is a commutative division algebra. An archaic name for a field is ...

Given a first-order ordinary differential equation (dy)/(dx)=F(x,y), (1) if F(x,y) can be expressed using separation of variables as F(x,y)=X(x)Y(y), (2) then the equation ...

In his monumental treatise Disquisitiones Arithmeticae, Gauss conjectured that the class number h(-d) of an imaginary quadratic field with binary quadratic form discriminant ...

Consider the recurrence relation x_n=(1+x_0^2+x_1^2+...+x_(n-1)^2)/n, (1) with x_0=1. The first few iterates of x_n are 1, 2, 3, 5, 10, 28, 154, ... (OEIS A003504). The terms ...

An important result in valuation theory which gives information on finding roots of polynomials. Hensel's lemma is formally stated as follows. Let (K,|·|) be a complete ...

Given a square n×n nonsingular integer matrix A, there exists an n×n unimodular matrix U and an n×n matrix H (known as the Hermite normal form of A) such that AU=H. ...