CMR 88 + 220 CHIA HẾT CHO 17
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![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(8^8+2^{20}\)
\(=\left(2^3\right)^8+2^{20}\)
\(=2^{24}+2^{20}\)
\(=2^{20}\left(2^4+1\right)\)
\(=2^{20}\cdot17⋮17\)
![](https://rs.olm.vn/images/avt/0.png?1311)
A = 8⁸ + 2²⁰
= (2³)⁸ + 2²⁰
= 2²⁴ + 2²⁰
= 2²⁰.(2⁴ + 1)
= 2²⁰.17 ⋮ 17
Vậy A ⋮ 17
![](https://rs.olm.vn/images/avt/0.png?1311)
Bài 1
a, cm : A = 165 + 215 ⋮ 3
A = 165 + 215
A = (24)5 + 215
A = 220 + 215
A = 215.(25 + 1)
A = 215. 33 ⋮ 3 (đpcm)
b,cm : B = 88 + 220 ⋮ 17
B = (23)8 + 220
B = 216 + 220
B = 216.(1 + 24)
B = 216. 17 ⋮ 17 (đpcm)
c, cm: C = 1 - 2 + 22 - 23 + 24 - 25 + 26 -...-22021 + 22022 : 6 dư 1
C=1+(-2+22-23+24- 25+26)+...+(-22017+22018-22019+22020-22021+22022)
C = 1 + 42 +...+ 22016.(-2 + 22 - 23 + 24 - 25 + 26)
C = 1 + 42+...+ 22016.42
C = 1 + 42.(20+...+22016)
42 ⋮ 6 ⇒ C = 1 + 42.(20+...+22016) : 6 dư 1 đpcm
![](https://rs.olm.vn/images/avt/0.png?1311)
a: \(G=8^8+2^{20}\)
\(=2^{24}+2^{20}\)
\(=2^{20}\left(2^4+1\right)=2^{20}\cdot17⋮17\)
b: Sửa đề: \(H=2+2^2+2^3+...+2^{60}\)
\(=2\left(1+2\right)+2^3\left(1+2\right)+...+2^{59}\left(1+2\right)\)
\(=3\left(2+2^3+...+2^{59}\right)⋮3\)
\(H=2+2^2+2^3+...+2^{60}\)
\(=2\left(1+2+2^2\right)+2^4\left(1+2+2^2\right)+...+2^{58}\left(1+2+2^2\right)\)
\(=7\left(2+2^4+...+2^{58}\right)⋮7\)
\(H=2+2^2+2^3+...+2^{60}\)
\(=\left(2+2^2+2^3+2^4\right)+...+\left(2^{57}+2^{58}+2^{59}+2^{60}\right)\)
\(=2\left(1+2+2^2+2^3\right)+...+2^{57}\left(1+2+2^2+2^3\right)\)
\(=15\left(2+2^5+...+2^{57}\right)⋮15\)
c: \(E=\left(1+3+3^2\right)+3^3\left(1+3+3^2\right)+...+3^{1989}\left(1+3+3^2\right)\)
\(=13\left(1+3^3+...+3^{1989}\right)⋮13\)
\(E=1+3+3^2+3^3+...+3^{1991}\)
\(=\left(1+3+3^2+3^3+3^4+3^5\right)+\left(3^6+3^7+3^8+3^9+3^{10}+3^{11}\right)+...+3^{1986}+3^{1987}+3^{1988}+3^{1989}+3^{1990}+3^{1991}\)
\(=364\left(1+3^6+...+3^{1986}\right)⋮14\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(1,8^8+2^{20}=2^{24}+2^{20}=2^{20}\left(2^4+1\right)=2^{20}\cdot17⋮17\)
\(2,A=\left(2+2^2\right)+\left(2^3+2^4\right)+...+\left(2^{119}+2^{120}\right)\\ A=2\left(1+2\right)+2^3\left(1+2\right)+...+2^{119}\left(1+2\right)\\ A=3\left(2+2^3+...+2^{119}\right)⋮3\)
\(A=\left(2+2^2+2^3\right)+...+\left(2^{118}+2^{119}+2^{120}\right)\\ A=2\left(1+2+2^2\right)+...+2^{118}\left(1+2+2^2\right)\\ A=\left(1+2+2^2\right)\left(2+...+2^{118}\right)=7\left(2+...+2^{118}\right)⋮7\\ A=\left(2+2^2+2^3+2^4\right)+...+\left(2^{117}+2^{118}+2^{119}+2^{120}\right)\\ A=2\left(1+2+2^2+2^3\right)+...+2^{117}\left(1+2+2^2+2^3\right)\\ A=\left(1+2+2^2+2^3\right)\left(2+...+2^{117}\right)=15\left(2+...+2^{117}\right)⋮15\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a, Ta có 16 5 + 2 15 = 2 4 5 + 2 15 = 2 20 + 2 15 = 2 15 2 5 + 1 = 2 15 . 33 chia hết cho 33
b, Ta có: 8 8 + 4 10 = 2 3 8 + 2 2 10 = 2 24 + 2 20 = 2 20 2 4 + 1 = 2 20 . 17 chia hết cho 17
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(8^8+2^{20}\)
\(=\left(2^3\right)^8+2^{20}\)
\(=2^{24}+2^{20}\)
\(=2^{20}.\left(2^4+1\right)\)
\(=2^{20}.17\)chia hết cho 17
88 + 220
= 224 + 220
= 220 ( 24 + 1 )
= 220 . 17 chia hết cho 17
Vậy 88 + 220 chia hết cho 17 ( đpcm )