0 should not be a primitive root

[Will Song]

Not sure if this is a known bug or not.

SageMath version 8.0, Release Date: 2017-07-21

sage: mod(0, 17).is_primitive_root()

True

The easy fix would just be to add

if self == 0:

    return True

after https://github.com/sagemath/sage/blob/master/src/sage/rings/finite_rings/integer_mod.pyx#L1586. This also fixes the issue with p^j being a primitive root mod p^k where p is an odd prime.

[Daniel Krenn]

This is now
https://trac.sagemath.org/ticket/23624

[Will Song]

Thanks for catching my mistake it should indeed be False instead of True.