M = (3^5+3^7+3^9)+(3^6+3^8+3^10)

   = 3^5.(1+3^2+3^4)+3^6.(1+3^2+3^4)

   = 3^5.91 + 3^6.91 = 91.(3^5+3^6) chia hết cho 91

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ありがとございます

Không hiểu

A = (3^5.1 + 3^5.3) + (3^7.1 + 3^7.3) + (3^9.1 + 3^9.3)

   = 3^5.(1+3) +  3^7.(1+3) + 3^9.(1+3)

   = 3^5.4 + 3^7.4 + 3^9.4

   =4.(3^5 +3^7 +3^9)

   =4.(3^5.1 +3^5.3^2 + 3^5.3^4)

   =4.3^5.(1+3^2+3^4)

   =4.243.(1+9+81)

   =972.91 chia hết cho 91

Vậy A chia hết cho 91

M=3^5*(1+3+3^2+3^3+3^4+3^5)

M=3^5*[(1+3^2+3^4)+(3+3^3+3^5)]

M=3^5*[91+273]

M=3^5*91*4

=>M chia het cho 91

=3^5(1+3+9)+3^8(1+3+9)

=13(3^5+3^8)

=13.3^5(1+3^3)

=13.3^5.28

=13.3^5.7.4

=>M chia hết cho 13 và 7 mà 13.7=91

=>M chia hết cho 91

ta có :91=7.13 vì (13,7)=1

ta chứng ming M chia hết cho 7 và 13 \(\Rightarrow\)M \(⋮\)91

CM M\(⋮\)7

CM M\(⋮\)13

\(\Rightarrow\)M\(⋮\)91

 M=3⁵+3⁶+3⁷+3⁸+3⁹+3¹⁰ 

= (3⁵+3⁶+3⁷)+(3⁸+3⁹+3¹⁰) 

=  3⁵.(1+3+3²) + 3⁸.(1+3+3²) 

 = 3⁵.13 + 3⁸.13

= 13.( 3⁵+3⁸​) 

= 13 . 3⁵ . (1+3³) 

= 13.3⁵. 28

= 13.7.3⁵.4 

= 91.3⁵.4 chia hết cho 91 

=> M chia hết cho 91 

A = 3⁵ + 3⁶ + 3⁷ + 3⁸ + 3⁹ + 3¹⁰

A = 3⁵( 1 + 3 + 3² + 3³ + 3⁴ + 3⁵ )

A = 3⁵ . 364

Vì 364\(⋮\)91 nên 3⁵. 364 \(⋮\)91

Hay A = 3⁵ + 3⁶ + 3⁷ + 3⁸ + 3⁹ + 3¹⁰ \(⋮\)91

\(6+6^2+\cdot\cdot\cdot+6^{10}\)

\(=6\cdot\left(1+6\right)+6^3\cdot\left(1+6\right)+\cdot\cdot\cdot+6^9\cdot\left(1+6\right)\)

\(=6\cdot7+6^3\cdot7+\cdot\cdot\cdot+6^9\cdot7\)

\(=7\cdot\left(6+6^3+\cdot\cdot\cdot+6^9\right)⋮7\)

\(\Rightarrow6+6^2+\cdot\cdot\cdot\cdot+6^{10}⋮7\)

\(5^1-5^9+5^8=5\left(1-5^8+5^7\right)⋮7\Leftrightarrow5^8-5^7-1⋮7\)

\(5\equiv-2\left(mod7\right)\Rightarrow5^3\equiv-1\left(mod7\right)\Rightarrow5^8\equiv4\left(mod7\right);5^7\equiv-2\left(mod7\right)\)

\(5^8-5^7-1\equiv5\left(mod7\right):v\)

\(6+6^2+\cdot\cdot\cdot+6^{10}\)

\(=6\cdot7+6^3\cdot7+\cdot\cdot\cdot+6^9\cdot7\)

\(=7\cdot\left(6+\cdot\cdot\cdot+6^9\right)\)

\(⋮7\)