[Toán 6] MTCT

H

hocvuima

1,Ta thấy: $2^{11}=2048\equiv 1(mod 23)$
Vậy $2^{999}=2^{990}.2^9\equiv 1.2^9(mod 23)$
\Rightarrow $2^{990}.2^9\equiv 1.512(mod 23)$
$2^{990}.2^9\equiv 1.6(mod 23)$
$2^{990}.2^9\equiv 6(mod 23)$
Vậy số dư của $2^{999}$ là 6
 
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