# Math Help - Primitive Elements

1. ## Primitive Elements

Good morning, one more question today:

w is a primitive element of Z_p (p prime)

for any a & b prove
w^a = w^b mod p iff a = b mod (p - 1)

Thanks again...

2. Originally Posted by cryptocrow
Good morning, one more question today:

w is a primitive element of Z_p (p prime)

for any a & b prove
w^a = w^b mod p iff a = b mod (p - 1)
If $w^a\equiv w^b \implies w^{a-b} \equiv 1$ since $w$ has order $p-1$ it means $p-1$ divides $a-b$.

3. thanks!