e., for any elements $a, b$ in the domain, we have $f(a * b) = f(a) * f(b)$, where $*$ denotes the group operation.
Now, let $f: Z_p \oplus Z_p \to Z_p$ be a homomorphism. We can write any element in $Z_p \oplus Z_p$ as $(a, b)$, where $a, b \in Z_p$. Since $Z_p$
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