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Thread: Find all the functions

  1. January 30th 2010, 04:50 PM #1
    Perelman
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    Find all the functions

    Hi !!

    Find all the functions : \mathbb{N} \longrightarrow \mathbb{N}, such as :

    \forall (m,n) \in \mathbb{N} : f(mn)=f(m).f(n) And f(2)=2

    f is strictly increasing of \mathbb{N} \longrightarrow \mathbb{N} .
    Last edited by CaptainBlack; January 30th 2010 at 11:10 PM.
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  2. January 31st 2010, 01:07 AM #2
    Shanks
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    Prove the following proposition by induction on n:
    For all natural numbers m\leq 2^n, f(m)=m.
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