4200:7=...
42005:7=...
36231:6=...
36228:6=...
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a.
\(2^{2024}=2^2.2^{2022}=4.\left(2^3\right)^{674}=4.8^{674}\)
Do \(8\equiv1\left(mod7\right)\Rightarrow8^{674}\equiv1\left(mod7\right)\)
\(\Rightarrow4.8^{674}\equiv4\left(mod7\right)\)
Hay \(2^{2024}\) chia 7 dư 4
b.
\(5^{70}+7^{50}=\left(5^2\right)^{35}+\left(7^2\right)^{25}=25^{35}+49^{25}\)
Do \(\left\{{}\begin{matrix}25\equiv1\left(mod12\right)\\49\equiv1\left(mod12\right)\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}25^{35}\equiv1\left(mod12\right)\\49^{25}\equiv1\left(mod12\right)\end{matrix}\right.\)
\(\Rightarrow25^{35}+49^{25}\equiv2\left(mod12\right)\)
Hay \(5^{70}+7^{50}\) chia 12 dư 2
c.
\(3^{2005}+4^{2005}=\left(3^5\right)^{401}+\left(4^5\right)^{401}=243^{401}+1024^{401}\)
Do \(\left\{{}\begin{matrix}243\equiv1\left(mod11\right)\\1024\equiv1\left(mod11\right)\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}243^{401}\equiv1\left(mod11\right)\\1024^{401}\equiv1\left(mod11\right)\end{matrix}\right.\)
\(\Rightarrow243^{401}+1024^{401}\equiv2\left(mod11\right)\)
Hay \(3^{2005}+4^{2005}\) chia 11 dư 2
d.
\(1044\equiv1\left(mod7\right)\Rightarrow1044^{205}\equiv1\left(mod7\right)\)
Hay \(1044^{205}\) chia 7 dư 1
e.
\(3^{2003}=3^2.3^{2001}=9.\left(3^3\right)^{667}=9.27^{667}\)
Do \(27\equiv1\left(mod13\right)\Rightarrow27^{667}\equiv1\left(mod13\right)\)
\(\Rightarrow9.27^{667}\equiv9\left(mod13\right)\)
hay \(3^{2003}\) chia 13 dư 9
6 + 6 + 6 + 6 + 6 + 6 + 6 + 6 + 6 + 7 + 7 + 7 + 7 + 7 = 89
k minh
Lời giải chi tiết:
7 > 6 | 2 < 5 | 7 > 3 | 6 = 6 |
7 > 4 | 5 < 7 | 3 > 1 | 6 < 7 |
7 > 2 | 2 < 7 | 7 > 1 | 7 = 7 |
6 x 4 = 24 12 : 6 = 2 7 x 3 = 21 63 : 7 = 9
7 x 5 = 35 42 : 7 = 6 6 x 8 = 48 48 : 6 = 8
6 x 6 = 36 28 : 7 = 4 7 x 8 = 56 49 : 7 = 7
6 x 4 = 24 12 : 6 = 02 7 x 3 = 21 63 : 7 = 09 7 x 5 = 35 42 : 7 = 06
6 x 8 = 48 48 :6 = 8 6 x 6 = 36 28 : 7 = 04 7 x 8 = 56 49 : 7 = 07
6 x 6 = 36 63 : 7 = 9 7 x 5 = 35 6 x 7 = 42
7 x 7 = 49 48 : 6 = 8 35 : 7 = 5 42 : 6 = 7
5 x 5 = 25 49 : 7 = 7 35 : 5 = 7 42 : 7 = 6
6 x 6 = .36.... 63 : 7 = 9..... 7 x 5 = .35...... 6 x 7 = ..42...
7 x 7 = ..42... 48 : 6 = ..8... 35 : 7 = ...5.. 42 : 6 = ..7...
5 x 5 = ...25.. 49 : 7 = .7.... 35 : 5 = ...7.. 42 : 7 = ..6...
hok tốt
4200 : 7 = 600
42005 : 7 = 6000 ( dư 5 )
36321 : 6 = 6053 ( dư 3 )
36228 : 6 = 6038
4200:7=6000
42005:7=6000 dư 5
36321:6=6053 dư 3
36228:6=6038