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NumberTheory

  

AreCoprime

  

test whether a sequence of numbers is relatively prime

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

AreCoprime(x1, x2, ..., xn)

AreCoprime(x1, x2, ..., xn, domain_opt)

Parameters

x1, x2, ..., xn

-

sequence of integers or Gaussian integers

domain_opt

-

(optional) an equation of the form domain = integer, domain = GaussInt, or domain = gaussian; the default is domain = integer

Description

• 

The AreCoprime function tests whether a sequence of numbers is relatively prime in a given domain. A sequence of numbers are relatively prime (or coprime) if the greatest common divisor of the numbers is equal to 1.

• 

By default, the test is performed in the integer domain (that is, domain = integer). To test whether a sequence of Gaussian integers is relatively prime, use either domain = GaussInt or domain = gaussian for domain_opt.

Examples

withNumberTheory:

The AreCoprime function tests if the greatest common divisor of a sequence of numbers is 1 or not. (The igcd function returns the greatest common divisor of a sequence of numbers.)

AreCoprime4,9

true

(1)

igcd4,9

1

(2)

AreCoprime14,21

false

(3)

igcd14,21

7

(4)

The domain_opt option can be used to specify the domain. In the following examples, the domain is the Gaussian integers. (The GaussInt:-GIgcd command returns the greatest common divisor of a sequence of Gaussian integers.)

AreCoprime1+2I,12I,domain=gaussian

true

(5)

GaussInt:-GIgcd1+2I,12I

1

(6)

AreCoprime3+5I,4+8I,domain=gaussian

false

(7)

GaussInt:-GIgcd3+5I,4+8I

1+I

(8)

The following visualizes the coprimes for the first fifteen integers in dark red:

matMatrix15,i,j`if`AreCoprimei,j,1,0

_rtable18446883718393065590

(9)

Statistics:-HeatMapmat,color=White,DarkRed

Compatibility

• 

The NumberTheory[AreCoprime] command was introduced in Maple 2016.

• 

For more information on Maple 2016 changes, see Updates in Maple 2016.

See Also

GaussInt

GaussInt[GIgcd]

igcd

NumberTheory

NumberTheory[InverseTotient]

NumberTheory[Totient]