\(C=\left(3+3^3+3^5\right)+\left(3^7+3^9+3^{11}\right)+...+\left(3^{1987}+3^{1989}+3^{1991}\right)\\ C=\left(3+3^3+3^5\right)+3^6\left(3+3^3+3^5\right)+...+3^{1986}\left(3+3^3+3^5\right)\\ C=\left(3+3^3+3^5\right)\left(1+3^6+...+3^{1986}\right)\\ C=273\left(1+3^6+...+3^{1986}\right)\\ C=13\cdot21\left(1+3^6+...+3^{1986}\right)⋮13\\ C=\left(3+3^3+3^5+3^7\right)+\left(3^9+3^{11}+3^{13}+3^{15}\right)+...+\left(3^{1985}+3^{1987}+3^{1989}+3^{1991}\right)\\ C=\left(3+3^3+3^5+3^7\right)+3^8\left(3+3^3+3^5+3^7\right)+...+3^{1984}\left(3+3^3+3^5+3^7\right)\\ C=\left(3+3^3+3^5+3^7\right)\left(1+3^8+...+3^{1984}\right)\\ C=2460\left(1+3^8+...+3^{1984}\right)\\ C=41\cdot60\left(1+3^8+...+3^{1984}\right)⋮41\)

A = 8⁸ + 2²⁰

= (2³)⁸ + 2²⁰

= 2²⁴ + 2²⁰

= 2²⁰.(2⁴ + 1)

= 2²⁰.17 ⋮ 17

Vậy A ⋮ 17

B = ( 3 + 3³ + 3⁵ ) + ( 3⁷ + 3⁹ + 3¹¹ ) + .... + ( 3¹⁹⁸⁷ + 3¹⁹⁸⁹ + 3¹⁹⁹¹ )

= 3 ( 1 + 3² + 3⁴ ) + 3⁷ ( 1 + 3² + 3⁴ ) + ... + 3¹⁹⁸⁷ ( 1 + 3² + 3⁴ )

= 3.(1 + 9 + 81) + 3⁷ (1 + 3² + 3⁴ ) + ... + 3¹⁹⁸⁷.( 1 + 3² + 3⁴ )

= 3.91 + 3⁷.91 + ... + 3¹⁹⁸⁷.91

= 91.( 3 + 3⁷ + ... + 3¹⁹⁸⁷ )

= 7.13( 3 + 3⁷ + ... + 3¹⁹⁸⁷ ) chia hết cho 13 ( đpcm )

CM chia hết cho 41 tương tự nha

giúp mình với mình chuẩn bị phải nộp bài rồi T~T 

\(B=2+2^2+2^3+...+2^{60}\)

\(=2\left(1+2+2^2\right)+...+2^{58}\left(1+2+2^2\right)\)

\(=7\cdot\left(2+...+2^{58}\right)⋮7\)

= 3( 1  + 3 + 3³) + 3⁵(1 + 3 + 3³) + ............+3¹⁹⁸⁹(1 + 3 + 3³) 

= 13( 3 + 3⁵ +........+ 3¹⁹⁸⁹) nên chia hết 13

Tham khảo

https://hoc24.vn/cau-hoi/c-3-33-35-31991-chia-het-cho-13-va-41.2492703297984

\(A=\left(3+3^2+3^3\right)+\left(3^4+3^5+3^6\right)+...+\left(3^{1989}+3^{1990}+3^{1991}\right)\\ A=3\left(1+3+3^2\right)+3^4\left(1+3+3^2\right)+...+3^{1989}\left(1+3+3^2\right)\\ A=\left(1+3+3^2\right)\left(3+3^4+...+3^{1989}\right)\\ A=13\left(3+3^4+...+3^{1989}\right)⋮13\)

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