Find all homomorphisms of the ring $ \mathbb{Z_6} $ in $ \mathbb{Z_{15}} $ (verification).

Question

So this is what I did

Will be homomorphism if and only if the two conditions are satisfied.

n= 6 m= 15 a ={1, 2, ...., 15}

i) an $\equiv$ 0 (mod m)

ii) a $\equiv$ $a^2$ (mod m)

The only two number that satisfies both conditions are 0 and 5.

I also use the formula ( $2^{w(l)-w(\frac{1}{(l,k)})}$ where l=15,k=6) to know how many numbers are homeomorphism and also got two.

Is this correct?