Question

CMR

81 mu 7 -27 mu 9 - 9 mũ 13 chia hết cho 45

Answer 1

\(81^7-27^9-9^{13}=\left(3^4\right)^7-\left(3^3\right)^9-\left(3^2\right)^{13}=3^{28}-3^{27}-3^{26}=3^{24}\left(81-27-9\right)=45.3^{24}⋮45\)

Answer 2

\(81^{27}-27^9-9^{13}\)

\(=3^{28}-3^{27}-3^{26}\)

\(=3^{26}\cdot5=3^{24}\cdot45\)Như vậy số này chia hết cho 45 . Suy ra 81 mũ 7 - 27 mũ 9 - 9 mũ 13 chia hết cho 45