# Homework Help: Counting the number of homorphisms

1. Aug 7, 2010

### seshikanth

1. The problem statement, all variables and given/known data
Hi,
I am trying to solve the following question:
count the number of homomorphism between Z/mZ and Z/nZ?
Can you tell me is my solution correct?

2. Relevant equations

3. The attempt at a solution
Let f be a homorphism.
f(mZ + a) = nZ + b ; a,b belong to G
Now, o(nZ+b) | n (from lagrangian theorem)
o(f(mZ+a)) = o(nZ+b); and o(f(mZ+a)) | o(mZ+a) which implies o(nZ+b) | m
Number of possiblities for o(nZ+b) = Number of common factors for m and n = Eulers Quotient for gcd(m,n)

Can you tell me if the approach correct? Because when i check the answers of the exercise question it is gcd(m,n) but here i am getting Euler's Qutient for gcd(m.n) = $$\varphi(gcd(m,n))$$

Thanks,
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution