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Functional equation

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 \(f(2001)\).

Note by Kalpa Roy
6 months, 3 weeks ago

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can anyone please help me out with this problem. Kalpa Roy · 6 months, 3 weeks ago

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@Kalpa Roy 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? Calvin Lin Staff · 6 months, 2 weeks ago

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