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NumberTheory

  

InverseTotient

  

inverse of Euler's totient function

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

InverseTotient(m)

Parameters

m

-

positive integer

Description

• 

The InverseTotient function returns the inverse image of Euler's totient function.

• 

Given a positive integer m, InverseTotient(m) returns the set of integers n that satisfy the equation Totient(n) = m.

Examples

withNumberTheory:

InverseTotient1

1,2

(1)

InverseTotient8

15,16,20,24,30

(2)

mapTotient,15,16,20,24,30

8

(3)

There are no numbers besides 1 and 2 with an odd totient.

InverseTotient3∪InverseTotient2347

(4)

`union`seqInverseTotienti,i=3..99,2

(5)

The following command plots the points (m, n), where n is a member of InverseTotient(m), for m from 1 to 1000.

plots:-pointplot`union`seqmapn→m,n,InverseTotientm,m=1..1000,labels=m,InverseTotient(m),labeldirections=horizontal,vertical,color=Fuchsia,symbol=circle

Compatibility

• 

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

• 

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

See Also

NumberTheory

NumberTheory[Totient]