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The Schur number S(k) is the largest integer n for which the interval [1,n] can be partitioned into k sum-free sets (Fredricksen and Sweet 2000). S(k) is guaranteed to exist ...

"The" Smarandache constant is the smallest solution to the generalized Andrica's conjecture, x approx 0.567148 (OEIS A038458). The first Smarandache constant is defined as ...

A solvable group is a group having a normal series such that each normal factor is Abelian. The special case of a solvable finite group is a group whose composition indices ...

The number of cells in a generalized Chinese checkers board (or "centered" hexagram). Unlike the polygonal numbers, there is ambiguity in the case of the star numbers as to ...

A star polygon {p/q}, with p,q positive integers, is a figure formed by connecting with straight lines every qth point out of p regularly spaced points lying on a ...

Surface area is the area of a given surface. Roughly speaking, it is the "amount" of a surface (i.e., it is proportional to the amount of paint needed to cover it), and has ...

Thâbit ibn Kurrah's rules is a beautiful result of Thâbit ibn Kurrah dating back to the tenth century (Woepcke 1852; Escott 1946; Dickson 2005, pp. 5 and 39; Borho 1972). ...

Let DeltaABC be a triangle and D a point on the side BC. Let I be the incenter, P the center of the circle tangent to the circumcircle and segments AD and BD, Q the center of ...

In database structures, two quantities are generally of interest: the average number of comparisons required to 1. Find an existing random record, and 2. Insert a new random ...

The spherical harmonics can be generalized to vector spherical harmonics by looking for a scalar function psi and a constant vector c such that M = del x(cpsi) (1) = psi(del ...