Question

Cho A=1+3+3^2+3^3+...+35. Tìm số dư khi chia A cho 40

Answer 1

A=3+32+33+34+...+325A=3+32+33+34+...+325

→A=(3+32+33+34+35)+(36+37+38+39+310)+...+(321+322+323+324+325)→A=(3+32+33+34+35)+(36+37+38+39+310)+...+(321+322+323+324+325)

→A=3(1+3+32+33+34)+36(1+3+32+33+34)+...+321(1+3+32+33+34)→A=3(1+3+32+33+34)+36(1+3+32+33+34)+...+321(1+3+32+33+34)

→A=(1+3+32+33+34)(3+36+...+321)→A=(1+3+32+33+34)(3+36+...+321)

→A=40(3+36+...+321)→A=40(3+36+...+321)

→A⋮40

Answer 2

A = 1 + 3 + 3² + 3³ + 3⁴ + 3⁵ + 3⁶ + 3⁷ + .... + 3³² + 3³³ + 3³⁴ + 3³⁵

    = (1 + 3 + 3² + 3³) + (3⁴ + 3⁵ + 3⁶ + 3⁷) + .... + (3³² + 3³³ + 3³⁴ + 3³⁵) 

    = (1 + 3 + 3² + 3³) + 3⁴.(1 + 3 + 3² + 3³) +.... + 3³².(1 + 3 + 3² + 3³) 

    = 40 + 3⁴.40 + ... + 3³².40

    = 40.(1 + 3⁴ + .... + 3³²) \(⋮\)40

=> A chia 4 dư 0