Question

[dream XD]

chứng minh rằng ( 8.3²⁰²¹+ 2²⁰²⁰ ) \(⋮\) 100 

Answer 1

[Trần Minh Hoàng]

+) Ta có \(2^{20}=\left(2^{10}\right)^2=1024^2=\overline{...76}\).

Ta thấy \(\overline{...76}.\overline{...76}=\overline{...76}\).

Do đó \(2^{2020}=\left(2^{20}\right)^{101}=\overline{...76}\).

+) Ta có \(3^{20}=\left(3^{10}\right)^2=\left(59049\right)^2=\overline{...01}\).

Ta thấy \(\overline{...01}.\overline{...01}=\overline{...01}\).

Do dó \(8.3^{2021}=\left(3^{20}\right)^{101}.24=\overline{...01}.24=\overline{...24}\).

Vậy \(8.3^{2021}+2^{2020}=\overline{...76}+\overline{...24}=\overline{...00}⋮100\).