Let ℕ = {1, 2, 3, . . .} be the set of all positive integers. Find all functions f : ℕ → ℕ such that for any positive integers a and b, the following two conditions hold: (1) f(ab) = f(a)f(b)(2) at least two of the numbers f(a), f(b) and f(a + b) are equal.
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