Khi chia STN a cho 24 thì được số dư là 10. Hỏi số a có chia hết cho 2 không, có chia hết cho 4 không , tìm số m nhỏ nhất chia hết cho 5
Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.



a ) \(A=\frac{5^{10}.9+5^{10}.7}{5^9.2^4}\)
\(A=\frac{5^{10}.\left(9+7\right)}{5^9.2^4}\)
\(A=\frac{5^{10}.16}{5^9.16}\)
\(A=5\)
b ) \(A=\frac{2^{10}.55+2^{10}.26}{2^8.27}\)
\(A=\frac{2^{10}.\left(55+26\right)}{2^8.27}\)
\(A=\frac{2^{10}.81}{2^8.27}\)
\(A=2^2.3=4.3=12\)
\(a)\)\(A=\frac{5^{10}.9+5^{10}.7}{5^9.2^4}\)
\(A=\frac{5^{10}.\left(9+7\right)}{5^9.2^4}\)
\(A=\frac{5^{10}.2^4}{5^9.2^4}\)
\(A=5\)
\(b)\)\(A=\frac{2^{10}.55+2^{10}.26}{2^8.27}\)
\(A=\frac{2^{10}.\left(55+26\right)}{2^8.27}\)
\(A=\frac{2^{10}.81}{2^8.27}\)
\(A=2^2.3\)
\(A=4.3=12\)
\(c)\)\(C=\frac{3.4.2^4.3.4.2^4}{5.2^5.4^2-16^2}\)
\(C=\frac{\left(3.4.2^4\right)^2}{5.2^5.4^2-16^2}\)
\(C=\frac{3^2.2^4.2^8}{5.2^5.2^4-2^8}\)
\(C=\frac{9.2^{12}}{5.2^9-2^8}\)
\(C=\frac{9.2^{12}}{2^8.\left(5.2-1\right)}\)
\(C=\frac{2^4}{1}\)
\(C=2^4=16\)


\(3.10^3+2.10^2+5.10\)
\(=10.\left(3.10^2+2.10+5\right)\)
\(=10.\left(3.100+20+5\right)\)
\(=10.325\)
\(=3250\)
Lời giải:
Giả sử số aa có nn chữ số. Đặt a=¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯a1a2..ana=a1a2..an¯
Theo bài ra ta có:
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯2019a1a2..an⋮20182019a1a2..an¯⋮2018
⇔2019.10n+¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯a1a2...an⋮2018⇔2019.10n+a1a2...an¯⋮2018
⇔10n+¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯a1a2..an⋮2018⇔10n+a1a2..an¯⋮2018
Vì 10n+¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯a1a2..an10n+a1a2..an¯ luôn dương nên để nó chia hết cho 20182018 thì 10n+¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯a1a2..an≥201810n+a1a2..an¯≥2018
⇒n≥4⇒n≥4
Để tìm aa min ta chọn nn min bằng 44
Khi đó 104+¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯a1a2a3a4⋮2018104+a1a2a3a4¯⋮2018
⇔1928+¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯a1a2a3a4⋮2018⇔1928+a1a2a3a4¯⋮2018
Do đó ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯a1a2a3a4=2018k−1928a1a2a3a4¯=2018k−1928 với k∈Nk∈N
Để a=¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯a1a2a3a4a=a1a2a3a4¯ min thì kk min
2018k−1928=¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯a1a2a3a4≥10002018k−1928=a1a2a3a4¯≥1000
⇒k≥1,45....⇒k≥2⇒k≥1,45....⇒k≥2 do k∈Nk∈N
Vậy kmin=2kmin=2
⇒amin=2018kmin−1928=2018.2−1928=2108⇒amin=2018kmin−1928=2018.2−1928=2108
Vậy.........
stn là j thế? 😌