Question

[Minz Ank]

Cho  A = 1.2.3......29.30 

        B = 31.32.33.......59.60

a) Chứng minh: B chia hết cho 2³⁰

b) Chứng minh: B - A chia hết cho 61 

Answer 1

[Akai Haruma]

a.

\(B=(32.34.36...60)(31.33.35....59)\)

\(=(2.16.2.17.2.18...2.30)(31.33.35...59)\)

\(=2^{15}(16.17.18...30)(31.33.35...59)\)

\(=2^{15}(16.18...30)(17.19.21...29)(31.33.35...59)\)

\(=2^{15}(2.8.2.9....2.15)(17.19..29)(31.33...59)\)

\(=2^{15}.2^8(8.9.10...15)(17.19...29)(31.33...59)\)

\(=2^{23}(8.10.12.14)(8.11.13.15).(17.19...29)(31.33...59)\)

\(=2^{23}.(8.10.12.14).T=2^{23}(2^3.2.5.2^2.3.2.7).T\)

\(=2^{23}.(2^7.105)T=2^{30}.105T\vdots 2^{30}\)

Answer 2

[Minz Ank]

Cô giúp e nốt phần b có đc ko ạ?