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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.
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