A function f : N --> N (where N denotes the set of positive integers) satisfies
(a) f(ab) = f(a)f(b) whenever the greatest common divisor of a and b is 1,
(b) f(p + q) = f(p) + f(q) for all prime numbers p and q.
Prove that f(2) = 2, f(3) = 3 and f(1999) = 1999.
As we're in the year 2014, calculate f(2014).
[adapted from IrMO 1999, Paper 2, Question 2]
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