If n Is Odd, Then gcd(n, n-2) = 1

Let \(\gcd(n, n-2) = d\):

$$ d|n $$$$ d|(n-2) $$

This means:

$$ d|n - (n-2) $$$$ d|2 $$

If \(d\) divides 2 and is odd, then \(d=1\).

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