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?
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]