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Let y_n be a complex number for 1<=n<=N and let y_n=0 if n<1 or n>N. Then (Montgomery 2001).

The (complete) gamma function Gamma(n) is defined to be an extension of the factorial to complex and real number arguments. It is related to the factorial by Gamma(n)=(n-1)!, ...

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 ...

A Brauer chain is an addition chain in which each member uses the previous member as an addend. A number n for which a shortest chain exists which is a Brauer chain is called ...

Elementary methods consist of arithmetic, geometry, and high school algebra. These are the only tools that may be used in the branch of number theory known as elementary ...

The lower matching number of a graph is the minimum size of a maximal independent edge set. The (upper) matching number may be similarly defined as the largest size of an ...

A multiple of a number x is any quantity y=nx with n an integer. If x and y are integers, then x is called a factor of y. The smallest positive number m for which there exist ...

The length of a number n in base b is the number of digits in the base-b numeral for n, given by the formula L(n,b)=|_log_b(n)_|+1, where |_x_| is the floor function. The ...

To color any map on the sphere or the plane requires at most six-colors. This number can easily be reduced to five, and the four-color theorem demonstrates that the necessary ...

For any ordinal number alpha, the successor of alpha is alpha union {alpha} (Ciesielski 1997, p. 46). The successor of an ordinal number alpha is therefore the next ordinal, ...