Inverse Element

Level pending

For the set of integers $$Z$$, an arithmetic operation $$\ast$$ is defined as $$a \ast b = a+b+2ab$$. How many elements of $$Z$$ have an inverse element for $$\ast$$? (The identity element is a value $$e$$ such that for all values $$n$$, $$e \ast n = n$$ and $$n \ast e = n .$$ The inverse element of $$n$$ is a value $$m$$ such that $$n \ast m = e$$ and $$m \ast n = e .$$)

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