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xyzt.10001=xyzt.10000+xyzt=xyztxyzt
Mà xyzt.10001=1a8bc9d7 => xyztxyzt = 1a8bc9d7
=> x=1, y=9, z=8, t=7.
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Ta có: abcd * 10001 = abcdabcd
=> xyzt * 10001 = xyztxyzt
=> xyztxyzt = 1a8bc9d7
=> x = 1
=> z = 8
=> y = 9
=> t = 7
Vậy xyzt = 1987
Ta có: abcd * 10001 = abcdabcd
=> xyzt * 10001 = xyztxyzt
=> xyztxyzt = 1a8bc9d7
=> x = 1
=> z = 8
=> y = 9
=> t = 7
Vậy xyzt = 1987
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Ta có : xyzt. 10001 = xyztxyzt
Mà xyzt . 10001 = 2a1bc0d4
Suy ra :x = 2 ; z = 1; y = 0 ; t = 4
Suy ra số xyzt = 2014
Vậy số cần tìm là 2014
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Bài giải
a) Ta có :
\(43^{43}-17^{17}=43^{40}\cdot43^3-17^{16}\cdot17=\left(43^4\right)^{10}\cdot43^3-\left(17^4\right)^4\cdot17=\overline{\left(...1\right)}^{10}\cdot\overline{\left(...3\right)}^3-\overline{\left(...1\right)}^4\cdot17\)
\(=\overline{\left(...1\right)}\cdot\overline{\left(...7\right)}-\overline{\left(...7\right)}=\overline{\left(...7\right)}-\overline{\left(...7\right)}=\overline{\left(...0\right)}\text{ }⋮\text{ }10\)
\(\Rightarrow\text{ ĐPCM}\)
xyzt = 1987
1987
ok