I have a group over $\mathbb Z$, defined by the binary operation $*$, such that $a*b:=a+b+2$.
From the previous exercise, I have deduced that the identity-element is $-2$ and that it is an abelian group under $\mathbb Z$, but the next exercise wants me to prove that it is isomorphic to the cyclic group $(\mathbb Z,+)$. But I dont really know how to write the answer. In the cyclic group $(\mathbb Z,+)$, you have that $(a,b)=a+b$, and in $(\mathbb Z,*)$ you have that $(a,b)=a+b+2$.
From my understaning, I must set up an homomorphism between those two groups $(\mathbb Z,+)$ which shows to be surjective and injective, but I'm a bit stuck.
Help would be appreciated.