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Apéry's constant is defined by zeta(3)=1.2020569..., (1) (OEIS A002117) where zeta(z) is the Riemann zeta function. Apéry (1979) proved that zeta(3) is irrational, although ...

A Pythagorean triple is a triple of positive integers a, b, and c such that a right triangle exists with legs a,b and hypotenuse c. By the Pythagorean theorem, this is ...

The AC method is an algorithm for factoring quadratic polynomials of the form p(x)=Ax^2+Bx+C with integer coefficients. As its name suggests, the crux of the algorithm is to ...

An arithmetic series is the sum of a sequence {a_k}, k=1, 2, ..., in which each term is computed from the previous one by adding (or subtracting) a constant d. Therefore, for ...

Cauchy's integral formula states that f(z_0)=1/(2pii)∮_gamma(f(z)dz)/(z-z_0), (1) where the integral is a contour integral along the contour gamma enclosing the point z_0. It ...

Let c and d!=c be real numbers (usually taken as c=1 and d=0). The Dirichlet function is defined by D(x)={c for x rational; d for x irrational (1) and is discontinuous ...

Let a convex polygon be inscribed in a circle and divided into triangles from diagonals from one polygon vertex. The sum of the radii of the circles inscribed in these ...

The extension ring obtained from a commutative unit ring (other than the trivial ring) when allowing division by all non-zero divisors. The ring of fractions of an integral ...

The logarithmic integral is defined as the Cauchy principal value li(x) = PVint_0^x(dt)/(lnt) (1) = ...

A riffle shuffle, also called the Faro shuffle, is a shuffle in which a deck of 2n cards is divided into two halves. The top half of the deck is placed in the left hand, and ...