How do you find the primitive roots of 31?

Answer 1

You need to know the base for the modulo arithmetic.

If the base is the integer p, then 31 can be expressed as n*p + r, or r is the remainder when 31 is divided by p. r is also called the primitive root of 31 modulo p.

The primitive root of 31, by itself, has no meaning. It is only in relation to p that it has a meaning and a value.

p = 2: primitive root = 1

p = 3: primitive root = 1

p = 4: primitive root = 3

p = 5: primitive root = 1

p = 7: primitive root = 3

p = 8: primitive root = 7

etc.