6. The function f is defined on the set of positive integers by f (1) = 1,
hand corner.
f (2n) = 2f (n), and nf (2n + 1) = (2n + 1)(f (n) + n) for all n ≥ 1.
Do not turn over until told to do so.
i) Prove that f (n) is always an integer.
ii) For how many positive integers less than 2007 is f (n) = 2n ?
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