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As originally stated by Gould (1972), GCD{(n-1; k),(n; k-1),(n+1; k+1)} =GCD{(n-1; k-1),(n; k+1),(n+1; k)}, (1) where GCD is the greatest common divisor and (n; k) is a ...

A Turing machine which, by appropriate programming using a finite length of input tape, can act as any Turing machine whatsoever. In his seminal paper, Turing himself gave ...

A problem posed by the Slovak mathematician Stefan Znám in 1972 asking whether, for all integers k>=2, there exist k integers x_1,...,x_k all greater than 1 such that x_i is ...

Simply stated, floating-point arithmetic is arithmetic performed on floating-point representations by any number of automated devices. Traditionally, this definition is ...

The Lambert W-function, also called the omega function, is the inverse function of f(W)=We^W. (1) The plot above shows the function along the real axis. The principal value ...

The spherical harmonics Y_l^m(theta,phi) are the angular portion of the solution to Laplace's equation in spherical coordinates where azimuthal symmetry is not present. Some ...

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 ...

An automorphism of a graph is a graph isomorphism with itself, i.e., a mapping from the vertices of the given graph G back to vertices of G such that the resulting graph is ...

The game of life is the best-known two-dimensional cellular automaton, invented by John H. Conway and popularized in Martin Gardner's Scientific American column starting in ...

A generalized quadrangle is a generalized polygon of order 4. An order-(s,t) generalized quadrangle contains s+1 points in each line and has t+1 lines through every point, ...