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M=2(1+2+2^2)+2^4(1+2+2^2)+2^7(1+2+2^2)
=7(2+2^4+2^7) chia hết cho 7
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a) 810 - 89 - 88 \(⋮\)55
\(\Rightarrow\)810 - 89 - 88 = 88 ( 82 - 8 - 1 )
\(\Rightarrow\)88 . 55 \(⋮\)55
b)817 - 279 - 913 \(⋮\)45
Ta có : 817 - 279 - 913 = 328 - 327 - 326 \(⋮\)45
\(\Rightarrow\)328 - 327 - 326 = 324 ( 34 - 33 - 32 )
\(\Rightarrow\)324 . 45\(⋮\)45
c) 76 + 75 - 74 \(⋮\)11
\(\Rightarrow\)76 + 75 - 74 = 74 ( 72 + 7 - 1 )
\(\Rightarrow\)74 . 5 . 11 \(⋮\)11
d) 109 + 108 + 107 \(⋮\)555
\(\Rightarrow\)109 + 108 + 107 = 106 ( 103 + 102 + 10 )
\(\Rightarrow\)106 . 2 . 555 \(⋮\)555
a) 8^10 - 8^9 - 8^8=8^8.64 - 8^8.8-8^8.1=8^8.(64-8-1)=8^8.55
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a) 55 -54 + 53 =53 ( 52 - 5 +1) =53 .21 \(⋮\)7 (vì 21 \(⋮\)7)
=> 55 - 54 + 53 \(⋮\)7
b) 109 + 108 +107 = 107 (102+10+1) = 107 .111= 106 .10. 111 = 106 .5. 222\(⋮\)222 (vì 222\(⋮\)222)
=> 109 + 108 + 107 \(⋮\)222
a)5^5-5^4+5^3=5^3.(5^2-5+1)=5^3.(25-5+1)=5^3.21 \(⋮\) 7(đpcm)
b) ta có 222=2.111
mà 10 chia hết cho 2
=>10^9+10^8+10^7 chia hết cho 2 (1)
lại có ;
10^9+10^8+10^7=10^7.(10^2+10+1)=10^7.111 (2)
từ 1 và 2 suy ra 10^9+10^8+10^7 chia hết cho 222
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e) \(81^7-27^9-9^{13}=3^{28}-3^{27}-3^{26}=3^{24}.\left(3^4-3^3-3^2\right)=3^{24}.45⋮45\left(Đpcm\right)\)
f) \(8^{10}-8^9-8^8=8^8.\left(8^2-8-1\right)=8^8.55⋮55\left(Đpcm\right)\)
g) \(10^9+10^8+10^7=10^7.\left(10^2+10+1\right)=10^7.111=5^6.2^7.555⋮555\left(Đpcm\right)\)
a) \(5^5-5^4+5^3=5^3.\left(5^2-5+1\right)=5^3.21⋮7\left(đpcm\right)\)
b) \(7^6+7^5-7^4=7^4.\left(7^2+7-1\right)=7^4.55⋮11\left(đpcm\right)\)
c) \(10^9+10^8+10^7=10^7.\left(10^2+10+1\right)=10^7.111=2^7.5^7.111=2^6.222.5^7\)\(⋮222\left(đpcm\right)\)
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a) Ta có: \(2^{12}-2^{10}+2^8=2^8\left(2^4-2^2+1\right)\)
\(=2^8.13\)
\(\Rightarrow2^{12}-2^{10}+2^8⋮13\)
Hok tốt nha^^
7^10+ 7^9- 7^8=78.72+78.7+78.1=78.(72+7-1)=78.55
=>7^10+ 7^9- 7^8 chia hết cho 55