Inverse Element

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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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