TTTTTTTTTTTTGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGTTTTTTTTTTTTTTTTGGGGGGGGGGGGGGGGGGGGGGTTTTTTTTTTTTGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGTTTTTTTTTTTTGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGTTTTTTTTTTTTGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGTTTTTTTTTTTTGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGTTTTTTTTTTTTGGGGGGGGGGGGGGGGGGTTTTTTTTTTTTGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGTTTTTTTTTTTTGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGTTTTTTTTTTTTGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGTTTTTTTTGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGTTTTTTTTTTTTGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGTTTTTTTTTTTTGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGTTTTTTTTTTTTTTTTGGGGGGGGGGGGGGGGGGGGGGTTTTTTTTTTTTGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGTTTTTTTTTTTTGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGTTTTTTTTTTTTGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGTTTTTTTTTTTTGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGTTTTTTTTTTTTGGGGGGGGGGGGGGGGGGTTTTTTTTTTTTGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGTTTTTTTTTTTTGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGTTTTTTTTTTTTGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGTTTTTTTTGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGTTTTTTTTTTTTGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGTTTTTTTTTTTTGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGTTTTTTTTTTTTTTTTGGGGGGGGGGGGGGGGGGGGGGTTTTTTTTTTTTGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGTTTTTTTTTTTTGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGTTTTTTTTTTTTGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGTTTTTTTTTTTTGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGTTTTTTTTTTTTGGGGGGGGGGGGGGGGGGTTTTTTTTTTTTGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGTTTTTTTTTTTTGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGTTTTTTTTTTTTGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGTTTTTTTTGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGTTTTTTTTTTTTGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGTTTTTTTTTTTTGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGTTTTTTTTTTTTTTTTGGGGGGGGGGGGGGGGGGGGGGTTTTTTTTTTTTGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGTTTTTTTTTTTTGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGTTTTTTTTTTTTGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGTTTTTTTTTTTTGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGTTTTTTTTTTTTGGGGGGGGGGGGGGGGGGTTTTTTTTTTTTGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGTTTTTTTTTTTTGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGTTTTTTTTTT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p là số nguyên tố lớn hơn 2 => p có dạng 4n + 1 và 4n - 1 ( c/m bổ đề phụ )

a) Xét 2 t/h xảy ra của p :

TH1 : p + 2017 = 4n + 1 + 2017 = 4n + 2018 = 2 ( 2n + 1009 ) chia hết cho 2 => hợp số

TH2 : p + 2017 = 4n - 1 + 2017 = 4n + 2016 = 2 ( 2n + 1008 ) chia hết cho 2 => hợp số 

b) tương tự xét 2 t/h của p

\(3^x.\left(\frac{1}{3}+2.3\right)=19\)

\(3^x.\frac{19}{3}=19\)

\(3^{x-1}.19=19\)

\(=>3^{x-1}=19:19=1\)

\(x-1=0=>x=1\)

Bài 1 : 

\(A=2^{12}.25^4=2^8.2^4.5^8=10^8.2^4=10^8.16\)

 \(10^8\) có 9 chữ số ( 1 chữ số 1 và 8 chữ số 0 ) 

Theo tính chất nhân 1 số tự nhiên với 10; 100; 1000; ... ;\(10^n\) ta có : 

\(a.10^n=\overline{a00...0}\) ( n chữ số 0 ) 

Suy ra \(10^8.16\) có 10 chữ số 

Vậy \(A\) có 10 chữ số 

Bài 2 : 

\(B=4+2^2+2^3+2^4+...+2^{35}\)

\(2\left(B-4\right)=2^3+2^4+2^5+...+2^{36}\)

\(2\left(B-4\right)-\left(B-4\right)=\left(2^3+2^4+2^5+...+2^{36}\right)-\left(2^2+2^3+2^4+...+2^{35}\right)\)

\(B-4=2^{36}-4\)

\(B=2^{36}\)

\(B=\left(2^{18}\right)^2\) là số chính phương 

Vậy \(B\) là số chính phương 

Chúc bạn học tốt ~ 

2^x+2 - 2^x = 96

<=> 2^x × 2² - 2^x = 96

<=> 2^x.( 2² - 1 ) = 96

<=> 2^x . 3 = 96

<=>  2^x = 96 : 3

<=>  2^x = 32

<=>  2^x = 2⁵

<=>  x   = 5

        Vậy x = 5 

\(=>\orbr{\begin{cases}\left(2x-3\right)^2=6^2\\\left(2x-3\right)^2=\left(-6\right)^2\end{cases}}\)

\(=>\orbr{\begin{cases}2x-3=6\\2x-3=-6\end{cases}}\)

\(=>\orbr{\begin{cases}2x=9\\2x=-3\end{cases}}\)

\(=>\orbr{\begin{cases}x=\frac{9}{2}\\x=-\frac{3}{2}\end{cases}}\)

( 2x - 3 ) ^2 = 36

(2x-3 ) ^2 = ( + - 6 ) ^2 

-> 2x-3 = +- 6

* 2x -3 =6                                  * 2x -3 = -6

2x = 9                                           2x= -3 

x= 9/2                                            x = -3 /2 

vậy x \(\in\)( 9/2 : -3 /2 )

ý b ) tự làm nha bạn , nó còn dễ hơn 1^ 2 

Để  111...1  + 2n chia hết cho 3 

thì \(\hept{\begin{cases}111...1\text{ }⋮\text{ }3\\2n\text{ }⋮\text{ }3\end{cases}}\)

Ta có 2n chia hết cho 3 

             mà 2 ko chia hết cho 3 

=> n chia hết cho 3 

Để 111...1 chia hết cho 3 <=> có n chữ số 1 

Vì 1 số có 1 dãy số toàn số 1 có hơn 3 chữ số thì chia hết cho 3 nên số còn lại cũng phải chia hết cho 3. 

Suy ra n = 1

anime

1. chấm màu xanh là những người đang on(giống như facebook đấy)

2.hình anime

- 

{\displaystyle 0^{n}=0\,}

{\displaystyle 1^{n}=1\,}

Trong trường hợp b = n là số nguyên dương, lũy thừa bậc n của a là tích của n thừa số bằng nhau, mỗi thừa số bằng a:

{\displaystyle a^{n}=\underbrace {a\times a\cdots \times a} _{n}}

Các tính chất quan trong nhất của lũy thừa với số mũ nguyên dương m, n là

{\displaystyle a^{m+n}=a^{m}\times a^{n}}

{\displaystyle a^{m-n}={\frac {a^{m}}{a^{n}}}}

{\displaystyle (a^{m})^{n}=a^{mn}}

{\displaystyle a^{m^{n}}=a^{(m^{n})}}

{\displaystyle (a\times b)^{n}=a^{n}\times b^{n}}

{\displaystyle ({\frac {a}{b}})^{n}={\frac {a^{n}}{b^{n}}}}

Đặc biệt, ta có:

{\displaystyle a^{1}=a}

lũy thừa bậc n của a là tích của n thừa số a 

các chữ số có tận cùng bằng 5 dều có chũ số tận cùng là 5 nhé

chúc bn hk tốt