Campus Livre
isPrimitiveRoot
Tests whether a is a primitive root modulo n.
Category: Mathematics > Number Theory
Syntax
tf = isPrimitiveRoot(a, n)Returns logical true where a is a primitive root modulo n.
Description
An integer a coprime to n is a primitive root modulo n when its powers run through every residue coprime to n, that is when the multiplicative order of a equals eulerPhi(n). Primitive roots exist only for n equal to 1, 2, 4, p^k or 2*p^k with p an odd prime.
Modulo 7 the primitive roots are 3 and 5.
Input arguments
a- Integer scalar or array of candidates.
n- Positive integer modulus.
Output arguments
tf- Logical array of the size of
a.
Example
Candidates modulo 7
isPrimitiveRoot(1:6, 7)
isPrimitiveRoot(2, 7)Output
ans = 1×6 logical array
0 0 1 0 1 0
ans = logical
0