Let \(f\) be a function defined as \(f: \mathbb N \to \mathbb N\), where \(\mathbb N\) denotes the set of natural numbers, and \(f\) satisfy the following conditions:

**(a)**: \(f(m) < f(n) \) for all \(m<n\).

**(b)**: \(f(2n) = f(n)+n\) for all positive integers \(n\).

**(c)**: \(n\) is a prime whenever \(f(n) \) is a prime.

Find \(f(2001)\).

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## Comments

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TopNewestcan anyone please help me out with this problem.

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What have you tried? What are your thoughts?

If we removed the 2nd condition, then there are a lot of possibilities, like making \(f(n) \) the nth prime. So, how can we make use of the 2nd condition?

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