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Stephen Wolfram
SEARCH MATHEMATICA 8 DOCUMENTATION
THIS IS DOCUMENTATION FOR AN OBSOLETE PRODUCT.
SEE THE
DOCUMENTATION CENTER
FOR THE LATEST INFORMATION.
Mathematica
>
Number Theoretic Functions
>
Built-in
Mathematica
Symbol
Integer and Number Theoretic Functions
Tutorials »
|
MultiplicativeOrder
EulerPhi
CarmichaelLambda
PowerMod
See Also »
|
Cryptographic Number Theory
Number Theoretic Functions
Number Theory
New in 6.0: Mathematical Functions
New in 6.0: Mathematics & Algorithms
New in 6.0: Number Theory & Integer Functions
More About »
PrimitiveRoot
PrimitiveRoot
[
n
]
gives a primitive root of
n
.
MORE INFORMATION
PrimitiveRoot
[
n
]
gives a generator for the multiplicative group of integers modulo
n
relatively prime to
n
.
PrimitiveRoot
[
n
]
returns unevaluated if
n
is not 2, 4, an odd prime power or twice an odd prime power.
EXAMPLES
CLOSE ALL
Basic Examples
(1)
A primitive root of the prime number 9 is 2:
In[1]:=
Out[1]=
The primitive root generates all integers modulo 9 that are relatively prime to 9:
In[2]:=
Out[2]=
Scope
(1)
Properties & Relations
(2)
Possible Issues
(1)
Neat Examples
(1)
SEE ALSO
MultiplicativeOrder
EulerPhi
CarmichaelLambda
PowerMod
TUTORIALS
Integer and Number Theoretic Functions
MORE ABOUT
Cryptographic Number Theory
Number Theoretic Functions
Number Theory
New in 6.0: Mathematical Functions
New in 6.0: Mathematics & Algorithms
New in 6.0: Number Theory & Integer Functions
New in 6
© 2013 Wolfram Research, Inc.
EXAMPLES
Basic Examples 
Scope 