GCD

Notations

Traditional name

Traditional notation

Mathematica StandardForm notation

Primary definition

Specific values

Specialized values

Values at fixed points

General characteristics

Domain and analyticity

gcd((Subscript[n, 1]),(Subscript[n, 2]),…,(Subscript[n, m])) is nonanalytical function defined on (ℤ^m)with values in ℤ.

Symmetries and periodicities

Parity

Permutation symmetry

Periodicity

No periodicity

Series representations

Generalized power series

Product representations

Generating functions

Transformations

Transformations and argument simplifications

Argument involving basic arithmetic operations

Multiple arguments

Identities

Functional identities

Summation

Finite summation

Infinite summation

Operations

Limit operation

Representations through more general functions

Through other functions

Representations through equivalent functions

With related functions

Inequalities

Theorems

Distribution of digits in the decimal expansion of the rational number

The decimal expansion of the rational number (p/q)/;gcd(p,q)==1 and b==(2^α)(5^β)R/;gcd(10,R)==1 has exactly max(α,β) nonrepeating and ν/;(10^ν)mod R==1 repeating digits.

The human hearing system

The human auditory perception of the pitch of two frequencies is the gcd of their frequencies.

History

Euclid

Copyright