Question

Tìm số dư khi chia B=2¹+2³+2⁵+2⁷+...+2²⁰¹⁵+2²⁰¹⁷ chia cho 21

Answer 1

B = 2¹ + 2³ + 2⁵ + ......+2²⁰¹⁵ + 2²⁰¹⁷

4B = 2² . ( 2¹ + 2³ + 2⁵ +.....+ 2²⁰¹⁵ + 2²⁰¹⁷ )

4B = 2³ + 2⁵ + 2⁷ + 2 ⁹ + ...... + 2²⁰¹⁹

4B - B = 2²⁰¹⁹ - 2¹

=> 3B = 2²⁰¹⁹ - 2¹

=> B = \(\frac{2^{2019}-2^1}{3}\)