Question

Chung minh rang S = 2 + 2⁵ + 2⁹ +...+ 2⁴¹ + 2⁴⁵ chia het cho 17

Answer 1

Sbằng(2+2^5)+(2^9+2^13)+.........+(2^41+2^45)

Sbằng2.(1+2^4)+2^9.(1+2^4)+......+2^41.(1+2^4)

Sbằng2.17+2^9.17+...........+2^41.17

S bằng(2+2^9+......+2^41).17 chia hết 17

^là mũ bạn nhé

Answer 2

=2.(2^4+1)+2^9.(2^4+1)...............+2^41.(2^4+1)

=2.17+2^9.17+..............+2^41.17

=17.(2+2^9+...........+2^41) chia hết cho 17 (đpcm)