• KingGeorge
[SOLVED] George's problem of the [insert arbitrary time unit] Define a function $$f: \mathbb{Z}^+ \longrightarrow \mathbb{Z}^+$$ such that $$f$$ is strictly increasing, is multiplicative, and $$f(2)=2$$. Show that $$f(n) =n$$ for all $$n$$. Hint 1: You need to find an upper and a lower bound for a certain $$n$$ and show that the bounds are the same. Hint 2: Find the upper and lower bound for $$n=18$$. Using this show that $$f(3)=3$$. Now deduce that $$f(n)=n$$ for all $$n$$. [EDIT: It should be noted that this problem is relatively difficult (but only if you don't see the right process)]
Mathematics

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