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Supposing that g(n)=n-2 for some n, we see that n is not 1 or 2, so that g(n) is even.

Therefore n=g(n)+2 is even. If we suppose that n has no odd prime divisors, then we find

that g(n)=n-2 implies n=4. So it remains to consider the case where n does have odd

prime divisors, and derive a contradiction. Can anyone furnish this elusive contradiction?

Thanks