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An integer n>1 is said to be highly cototient if the equation x-phi(x)=n has more solutions than the equations x-phi(x)=k for all 1<k<n, where phi is the totient function. ...

The set of numbers generated by excluding the sums of two or more consecutive earlier members is called the prime numbers of measurement, or sometimes the segmented numbers. ...

Given a Lucas sequence with parameters P and Q, discriminant D!=0, and roots a and b, the Sylvester cyclotomic numbers are Q_n=product_(r)(a-zeta^rb), (1) where ...

For every positive integer n, there is a unique finite sequence of distinct nonconsecutive (not necessarily positive) integers k_1, ..., k_m such that ...

1. A straight line segment can be drawn joining any two points. 2. Any straight line segment can be extended indefinitely in a straight line. 3. Given any straight line ...

A hexagon is a six-sided polygon. Several special types of hexagons are illustrated above. In particular, a hexagon with vertices equally spaced around a circle and with all ...

Flat polygons embedded in three-space can be transformed into a congruent planar polygon as follows. First, translate the starting vertex to (0, 0, 0) by subtracting it from ...

A circle packing is called rigid (or "stable") if every circle is fixed by its neighbors, i.e., no circle can be translated without disturbing other circles of the packing ...

An improper use of the symbol sqrt(-1) for the imaginary unit leads to the apparent proof of a false statement. sqrt(-1) = sqrt(-1) (1) sqrt((-1)/1) = sqrt(1/(-1)) (2) ...

The Platonic solids, also called the regular solids or regular polyhedra, are convex polyhedra with equivalent faces composed of congruent convex regular polygons. There are ...