có: đặt vế trái = O
=> [tex]O=1+x+x^2+...+x^{31}\\\\ <=> Ox=x+x^2+x^3+...+x^{32}\\\\ <=> O.(x-1)=x^{32}-1\\\\ <=> O=\frac{x^{32}-1}{x-1}[/tex]
đặt vế phải =N
=> [tex]N=(1+x).(1+x^2)+...+(1+x^{16})\\\\ <=> (x-1)N=(x-1).(x+1).(x^2+1)+...+(x^{16}+1)\\\\ =(x^2-1).(x^2+1).(x^4+1).(x^8+1).(x^{16}+1)\\\\ =(x^4-1).(x^4+1).(x^8+1).(x^{16}+1)\\\\ =(x^8-1).(x^8+1).(x^{16}-1)\\\\ =(x^{16}-1).(x^{16}+1)\\\\ =x^{32}-1[/tex]
=> đpcm