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a )
Ta có :
87 - 218 = ( 23 )7 - 218= 221 - 218 = 218 ( 23 - 1 ) = 218 . 7 = 217 .2.7 = 217 . 14 ( chia hết cho 14 )
Vậy 87-218chia hết cho 14
b )
Ta có 106 - 57 = 26 . 56 - 57
= 56 . (26 - 5)
= 56 . (64 - 5)
= 56 . 59 chia hết cho 59
Vậy 106 - 57 chia hết cho 59
c )
\(8^7-2^{18}=\left(2^3\right)^7-2^{18}=2^{21}-2^{18}=2^{17}.\left(2^4-2\right)=2^{17}.14⋮14.\)
\(10^6-5^7=\left(2.5\right)^6-5^7=2^6.5^6-5^7=5^6.\left(2^6-5\right)=5^5.59⋮59.\)
a) Ta có : \(8^7-2^{18}=\left(2^3\right)^7-2^{17+1}\)
\(\Rightarrow8^7-2^{18}=2^{3\times7}-2^{17}\times2^1\)
\(\Rightarrow8^7-2^{18}=2^{21}-2^{17}\times2\)
\(\Rightarrow8^7-2^{18}=2^{17+4}-2^{17}\times2\)
\(\Rightarrow8^7-2^{18}=2^{17}\times2^4-2^{17}\times2\)
\(\Rightarrow8^7-2^{18}=2^{17}\left(2^4-2\right)\)
\(\Rightarrow8^7-2^{18}=2^{17}\left(16-2\right)\)
\(\Rightarrow8^7-2^{18}=2^{17}\times14\)
\(\Rightarrow\left(8^7-2^{18}\right)⋮14\left(\text{vì }14⋮14\right)\)
b) Ta có : \(10^6-5^7=\left(2\times5\right)^6-5^{6+1}\)
\(\Rightarrow10^6-5^7=2^6\times5^6-5^6\times5^1\)
\(\Rightarrow10^6-5^7=5^6\left(2^6-5^1\right)\)
\(\Rightarrow10^6-5^7=5^6\left(64-5\right)\)
\(\Rightarrow10^6-5^7=5^6\times59\)
\(\Rightarrow\left(10^6-5^7\right)⋮59\left(\text{vì }59⋮59\right)\)
a) 106 - 57
= 26 . 56 - 57
= 56 . (26 - 5)
= 56 . (64 - 5)
= 56 . 59 chia hết cho 59
=> đpcm
b) 817 - 279 - 913
= (34)7 - (33)9 - (32)13
= 328 - 327 - 326
= 326 .(32 - 3 - 1)
= 326 . (9 - 3 - 1)
= 324 . 32 . 5
= 324 . 9 . 5
= 324 . 45 chia hết cho 45
=> đpcm
c) 87 - 218
= (23)7 - 218
= 221 - 218
= 218 . (23 - 1)
= 218 (8 - 1)
= 217 . 2 . 7
= 217 . 14 chia hết cho 14
=> đpcm
d) 109 + 108 + 107
= 107 . (102 + 10 + 1)
= 57 . 27 . (100 + 10 + 1)
= 57 . 26 . 2 . 111
= 57 . 26 . 222 chia hết cho 222
=> đpcm
b: \(8^{12}-2^{33}-2^{30}\)
\(=2^{36}-2^{33}-2^{30}\)
\(=2^{30}\left(2^6-2^3-1\right)=2^{30}\cdot55⋮55\)
c: \(8^7-2^{18}=2^{21}-2^{18}\)
\(=2^{18}\left(2^3-1\right)=2^{17}\cdot14⋮14\)
d: \(10^6-5^7\)
\(=2^6\cdot5^6-5^7\)
\(=5^6\left(2^6-5\right)=5^6\cdot59⋮59\)
a: \(8^7-2^{18}=2^{21}-2^{18}=2^{18}\cdot7=2^{17}\cdot14⋮14\)
b: \(10^6-5^7=5^6\cdot2^6-5^7=5^6\cdot\left(2^6-5\right)=5^6\cdot59⋮59\)
a, Ta có :
\(8^7-2^{18}\)
\(=\left(2^3\right)^7-2^{18}\)
\(=2^{21}-2^{18}\)
\(=2^{18}\left(2^3-1\right)\)
\(=2^{18}.7\)
\(=2^{17}.2.7\)
\(=2^{17}.14⋮14\)
\(\Leftrightarrow8^7-2^{18}⋮14\rightarrowđpcm\)
b, \(10^6-5^7\)
\(=\left(2.5\right)^6-5^7\)
\(=2^6.5^6-5^7\)
\(=2^6.5^6-5^6.5\)
\(=5^6\left(2^6-5\right)\)
\(=5^6.59⋮59\)
\(\Leftrightarrow10^6-5^7⋮59\rightarrowđpcm\)
\(8^7-2^{18}\)
\(=\left(2^3\right)^7-2^{18}\)
\(=2^{21}-2^{18}\)
\(=2^{18}.2^3-2^{18}.1\)
\(=2^{18}.\left(2^3-1\right)\)
\(=2^{18}.7\)
\(=2^{17}.14⋮14\rightarrowđpcm\)
\(10^6-5^7\)
\(=\left(2.5\right)^6-5^7\)
\(=2^6.5^6-5^7\)
\(=64.5^6-5^6.5\)
\(=5^6\left(64-5\right)\)
\(=5^6.59⋮59\rightarrowđpcm\)