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Question Number 71868 by naka3546 last updated on 21/Oct/19

Commented by prakash jain last updated on 21/Oct/19

$$f\left(n\right)=0$$

Commented by mr W last updated on 21/Oct/19

$$whatiff\left(f\left(n\right)\right)=4n?$$

Commented by Cmr 237 last updated on 21/Oct/19

$$premierementtudoitpreciser$$$$quefestcroissante!$$$$nowwehaveprovethat$$$$f\left(1\right)=2andf\left(2\right)=3$$$$\mathit{p}\mathit{r}\mathit{o}\mathit{v}\mathit{e}:$$$$supposonsquef\left(1\right)=k$$$$-ifk<2wehave$$$$f\left(1\right)<2\Rightarrow f\left(1\right)⩽1ief\searrow$$$$absurdecarf\nearrow pardefinition.$$$$-ifk=3$$$$f\left(1\right)=3\Rightarrow f\left(f\left(1\right)\right)=f\left(3\right)=3$$$$absurdecarf\nearrow$$$$-ifk>3wehave$$$$f\left(f\left(1\right)\right)=f\left(k\right)=3absurdecarf\nearrow$$$$doncf\left(1\right)=2$$$$genalement,pour0<q<3^k$$$$f(3^k+q)=2\times 3^k+qet$$$$f(2\times 3^k+q)=3^{k+1}+3q$$$$2019=2\times 3^6+561$$$$f\left(2019\right)=3^7+3\times 561$$$$=3870$$$$$$$$$$

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