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Question Number 75569 by naka3546 last updated on 12/Dec/19

Commented by MJS last updated on 13/Dec/19

$$\mathrm{was}\mathrm{my}\mathrm{answer}\mathrm{to}\mathrm{the}\mathrm{other}\mathrm{one}\mathrm{ok}?$$$${\mathrm{it}}^{\prime }\mathrm{s}\mathrm{hard}\mathrm{to}\mathrm{understand}...$$

Commented by naka3546 last updated on 13/Dec/19

$${2019}^n=.....abcde$$$${2019}^m=.....abcde$$$$min\{m+n\}=?$$

Commented by MJS last updated on 13/Dec/19

$$\mathrm{so}\mathrm{we}\mathrm{have}$$$$a_{n+1}=\mathrm{fpart}\left(2019a_n\right)$$$$a_0=.00001$$$$\mathrm{and}{\mathrm{we}}^{\prime }\mathrm{re}\mathrm{asking}\mathrm{for}\mathrm{the}\mathrm{length}\mathrm{of}\mathrm{the}\mathrm{period}$$$$\mathrm{of}\mathrm{this}\mathrm{series}$$

Commented by MJS last updated on 13/Dec/19

$${\mathrm{I}}^{\prime }\mathrm{m}\mathrm{testing}$$$$a_0=.00001$$$$a_{50}=.89001$$$$a_{100}=.78001$$$$...$$$$a_{500}=.90001$$$$\Rightarrow a_{5000}=.00001$$$$\mathrm{I}\mathrm{think}\mathrm{this}\mathrm{goes}\mathrm{for}\mathrm{any}{a}_n=.bcdef$$$$a_n=a_{n+5000}=.bcdef$$$$\Rightarrow \min (m+n)=5000\mathrm{if}\mathrm{we}\mathrm{allow}m=0$$$$\mathrm{or}\min (m+n)=5002\mathrm{if}m>0$$

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