Question Number 130426 by Koyoooo last updated on 25/Jan/21
Answered by Olaf last updated on 25/Jan/21
$$\left(\mathrm{9}×\mathrm{9}×\mathrm{9}×\mathrm{9}\right)_{\mathrm{10}} \:=\:\mathrm{100}_{\mathrm{81}} \\ $$$$\mathrm{9}^{\mathrm{4}} \:\mathrm{en}\:\mathrm{base}\:\mathrm{10}\:\mathrm{egale}\:\mathrm{100}\:\mathrm{en}\:\mathrm{base}\:\mathrm{81} \\ $$
Answered by Olaf last updated on 25/Jan/21
$$\left(\mathrm{9}+\mathrm{9}+\mathrm{9}+\mathrm{9}\right)_{\mathrm{10}} \:=\:\mathrm{100}_{\mathrm{6}} \\ $$$$\left(\mathrm{9}+\mathrm{9}+\mathrm{9}+\mathrm{9}\right)_{\mathrm{25}} \:=\:\mathrm{100}_{\mathrm{9}} \\ $$$$\left(\mathrm{9}+\mathrm{9}+\mathrm{9}+\mathrm{9}\right)_{\mathrm{46}} \:=\:\mathrm{100}_{\mathrm{12}} \\ $$$$\left(\mathrm{9}+\mathrm{9}+\mathrm{9}+\mathrm{9}\right)_{\mathrm{73}} \:=\:\mathrm{100}_{\mathrm{15}} \\ $$$$\left(\mathrm{9}+\mathrm{9}+\mathrm{9}+\mathrm{9}\right)_{\mathrm{106}} \:=\:\mathrm{100}_{\mathrm{18}} \\ $$$$\left(\mathrm{9}+\mathrm{9}+\mathrm{9}+\mathrm{9}\right)_{\mathrm{145}} \:=\:\mathrm{100}_{\mathrm{21}} \\ $$$$... \\ $$$$\left(\mathrm{100}\right)_{\mathrm{3}{n}+\mathrm{6}} \:=\:\left(\mathrm{9}+\mathrm{9}+\mathrm{9}+\mathrm{9}\right)_{\mathrm{3}\left({n}+\mathrm{2}\right)^{\mathrm{2}} −\mathrm{2}} \\ $$