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## Homework Statement

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?

## Homework Equations

## 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) = [tex]\varphi(gcd(m,n))[/tex]

Thanks,