Question

CHỨNG TỎ RẰNG :

a) A=2+2^2+2^3+2^4+...+2^10 CHIA HẾT CHO 31

b)B=12^1980-2^1000 CHIA  HẾT CHO 10

Answer 1

a) A = \(\left(2+2^2+2^3+...+2^5\right)+\left(2^6+2^7+...+2^{10}\right)\)

\(=\left(2.31\right)+2^5.31=31.\left(2+2^5\right)\)

Vậy A chia hết cho 31