What would a direct proof look like? Since the statement starts with a universal quantifier, we would start by, ``Let \(n\) be an arbitrary integer." The rest of the statement is an implication. In a direct proof we assume the “if” part, so the next line would be, “Assume \(n\) is greater than 2 and is even.” I have no idea what comes next, but eventually, we would need to find two prime numbers \(p\) and \(q\) (depending on \(n\)) and explain how we know that \(n = p+q\text{.}\)
in-context