16⁵ - 2¹⁵

= (2⁴)⁵ - 2¹⁵

= 2²⁰ - 2¹⁵

= 2¹⁵(2⁵ - 1)

= 2¹⁵.31 \(⋮31\)(đpcm)

\(16^5-2^{15}=\left(2^4\right)^5-2^{15}=2^{20}-2^{15}=2^{15}\left(2^5-1\right)=31.2^{12}⋮31\)

ta có : \(16^5=\left(2^4\right)^5=2^{20}\)

=> \(2^{20}-2^{15}=2^{15}\left(2^5-1\right)\)     

                         \(=2^{15}\left(32-1\right)\)  

                         \(=2^{15}.31\) chia hết cho 31

Ta có:

16⁵ - 2¹⁵ = (2⁴)⁵ - 2¹⁵

= 2²⁰ - 2¹⁵

= 2¹⁵ .( 2⁵ - 1)

= 2¹⁵ . 31

Vì 31 chia hết cho 31 nên 2¹⁵ . 31 chia hết cho 31 hay 16⁵ - 2¹⁵ chia hết cho 31 (dpcm)

Ta có:

16⁵ - 2¹⁵

= (2⁴)⁵ - 2¹⁵

= 2⁵ . 2¹⁵ - 2¹⁵

= 2¹⁵(32 - 1) \(⋮\) 31(đpcm)

Ta có:16⁵ -2¹⁵=(2⁴)⁵-2¹⁵

=2²⁰-2¹⁵

=2⁵=31

=>31 chia hết cho 31

a) \(5+5^2+5^3+....+5^{100}\)

đặt \(A=5+5^2+5^3+....+5^{100}\) ( \(A\) có \(100\) số hạng )

\(A=\left(5+5^2\right)+\left(5^3+5^4\right)+....+\left(5^{99}+5^{100}\right)\) ( có \(100\div2=50\) nhóm )

\(A=5\left(1+5\right)+5^3\left(1+5\right)+....+5^{99}\left(1+5\right)\)

\(A=5.6+5^3.6+....+5^{99}.6\)

\(A=6\left(5+5^3+....+5^{99}\right)\)

vì \(6⋮6\Rightarrow6\left(5+5^3+....+5^{99}\right)⋮6\Rightarrow A⋮6\)

b) \(2+2^2+2^3+....+2^{100}\)

đặt \(B=2+2^2+2^3+....+2^{100}\) ( \(B\) có \(100\) số hạng )

\(B=\left(2+2^2+2^3+2^4+2^5\right)+.....+\left(2^{96}+2^{97}+2^{98}+2^{99}+2^{100}\right)\) ( có \(100\div5=20\) nhóm )

\(B=2\left(1+2+2^2+2^3+2^4\right)+....+2^{96}\left(1+2+2^2+2^3+2^4\right)\)

\(B=2.31+....+2^{96}.31\)

\(B=31\left(2+...+2^{96}\right)\)

vì \(31⋮31\Rightarrow31\left(2+...+2^{96}\right)\Rightarrow B⋮31\)

a) 5+5^2+5^3..+5^100

=(5+5^2)+(5^3+5^4)+....+(5^99+5^100)

=5.(1+5)+5^3.(1+5)+....+5^99.(1+5)

=5.6+5^3.6+.....+5^99.6

=6.(5+5^3+.....+5^99):6

cau b tuong tu nhe ban

ủng hộ mình lên 360 điểm nha các bạn

\(16^5-2^{15}.\)

\(=\left(2^4\right)^5-2^{15}.\)

\(=2^{20}-2^{15.}\)

\(=2^{15}\left(2^5-1\right).\)

\(=2^{15}\left(32-1\right).\)

\(=2^{15}.31⋮31\left(đpcm\right).\)

1, Có : 16^5 - 2^15 = (2^4)^5 - 2^15 = 2^20 - 2^15 = 2^15 . (2^5-1) = 2^15 . 31 chia hết cho 31

k mk nha

1)

 \(16^5+2^{15}⋮33\)

\(=\left(2^4\right)^5+2^{15}\)

\(=2^{20}+2^{15}\)

\(=2^{15}.\left(1+2^5\right)\)

\(=2^{15}.33⋮33\)

(2^4)^5-2^15=2^20-2^15

                    =1015808:31

                    =32768

vậy 16^5-2^15 chia hết cho 31

dấu ^ là mũ nha bạn

`5^14 + 5^15 + 5^16 = 5^14 . (1+5+5^2) = 5^14 . 31 vdots 31`.

a) 5¹⁴ +5¹⁵ +5¹⁶

=5¹⁴ ( 1 + 5 +5²)

=5¹⁴ ( 1 + 5 +25)

=5¹⁴ . 31 

Mà 31 \(⋮\)31 nên (5¹⁴ . 31) \(⋮31\)