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Gaussian primes are Gaussian integers z=a+bi satisfying one of the following properties. 1. If both a and b are nonzero then, a+bi is a Gaussian prime iff a^2+b^2 is an ...

If two single-valued continuous functions kappa(s) (curvature) and tau(s) (torsion) are given for s>0, then there exists exactly one space curve, determined except for ...

Synthetic division is a shortcut method for dividing two polynomials which can be used in place of the standard long division algorithm. This method reduces the dividend and ...

A two-dimensional grid graph, also known as a rectangular grid graph or two-dimensional lattice graph (e.g., Acharya and Gill 1981), is an m×n lattice graph that is the graph ...

The substitution of x=w-p/(3w) (1) into the standard form cubic equation x^3+px=q. (2) The result reduces the cubic to the equation w^3-(p^3)/(27w^3)-q=0, (3) which is easily ...

A ring without zero divisors in which an integer norm and an associated division algorithm (i.e., a Euclidean algorithm) can be defined. For signed integers, the usual norm ...

An arrangement of points with no three collinear, or of lines with no three concurrent.

Regardless of where one white and one black square are deleted from an ordinary 8×8 chessboard, the reduced board can always be covered exactly with 31 dominoes (of dimension ...

Two groups G and H are said to be isoclinic if there are isomorphisms G/Z(G)->H/Z(H) and G^'->H^', where Z(G) is the group center of the group, which identify the two ...

Any irreducible curve may be carried by a factorable Cremona transformation into one with none but ordinary singular points.