Group homomorphisms

Homomorphism
Problem 1:

Find all group homomorphisms from Z4 into Z10

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.... Then the formula µ([x]n) = [mx]k, for all [x]n in Zn, defines a homomorphism. Furthermore, every homomorphism from Zn into Zk must be of this form. The image µ(Zn) is the cyclic subgroup generated by ...