galois.is_primitive_root

galois.is_primitive_root(g, n)

Determines if \(g\) is a primitive root modulo \(n\).

\(g\) is a primitive root if the totatives of \(n\), the positive integers \(1 \le a < n\) that are coprime with \(n\), can be generated by powers of \(g\).

Parameters

• g (int) – A positive integer that may be a primitive root modulo \(n\).

• n (int) – A positive integer.

Returns

True if \(g\) is a primitive root modulo \(n\).

Return type

bool

Examples

In [1]: galois.is_primitive_root(2, 7)
Out[1]: False

In [2]: galois.is_primitive_root(3, 7)
Out[2]: True

In [3]: galois.primitive_roots(7)
Out[3]: [3, 5]