Question

M=3^5+3^6+3^7+3^8+3^9+3^10.Chứng minh M chia hết cho 91

Answer 1

M= 3^5(1+3+3^2+3^3+3^4+3^5) M=3^5(1+3+9+27+81+243) M=3^5(364)=3^5.4.91 hay M chia hết cho 91

Answer 2

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

Answer 3

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