Question

Chứng minh (36^{36 _} 9¹⁰) chia hết cho 45

Answer 1

Ta có : \(36^{36}=\left(4.9\right)^{36}=4^{36}.9^{36}⋮9\)(1)

\(9^{10}⋮9\)(2)

Từ (1); (2) => \(36^{36}-9^{10}⋮9\) (3)

Ta có : \(36^{36}=\left(6^2\right)^{36}=6^{72}=\overline{.....6}\)

\(9^{10}=\overline{......1}\)

\(\Rightarrow36^{36}-9^{10}=\overline{......6}-\overline{......1}=\overline{......5}⋮5\) (4)

Từ (3) ; (4) \(\Rightarrow36^{36}-9^{10}⋮5;9\) Mà \(\left(5;9\right)=1\) \(\Rightarrow36^{36}-9^{10}⋮45\) (đpcm)