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If there is an integer 0<x<p such that x^2=q (mod p), (1) i.e., the congruence (1) has a solution, then q is said to be a quadratic residue (mod p). Note that the trivial ...

A dozen dozen, also called a gross. 144 is a square number and a sum-product number.

If an aliquot sequence {s^0(n),s(n),s^2(n),...} for a given n is bounded, it either ends at s(1)=0 or becomes periodic. If the sequence is periodic (or eventually periodic), ...

A Bergman kernel is a function of a complex variable with the "reproducing kernel" property defined for any domain in which there exist nonzero analytic functions of class ...

A Bloch vector is a unit vector (cosphisintheta, sinphisintheta, costheta) used to represent points on a Bloch sphere.

For every positive integer n, there exists a square in the plane with exactly n lattice points in its interior. This was extended by Schinzel and Kulikowski to all plane ...

A set of planes sharing a point in common. For planes specified in Hessian normal form, a bundle of planes can therefore be specified as ...

A clear-cut way of describing every object in a class in a one-to-one manner.

The orthotomic of the unit circle represented by x = cost (1) y = sint (2) with a source at (x,y) is x_o = xcos(2t)-ysin(2t)+2sint (3) y_o = -xsin(2t)-ycos(2t)+2cost. (4)

In a cochain complex of modules ...->C^(i-1)->^(d^(i-1))C^i->^(d^i)C^(i+1)->..., the module B^i of i-coboundaries is the image of d^(i-1). It is a submodule of C^i and is ...