Question

chứng minh rằng:

2¹⁹⁹⁵-1 chia hết cho 31

(làm bằng cách đồng dư nhé)

Answer 1

2^1995 - 1 = ( 2^5)^399 = 32^399 -1

Ma 32 dong du vs 1( mod 31 )

=> 32^399 dong du vs 1( mod 31 )

=> 32^399 dong du vs 0( mod 31 )

=> 2^1995 - 1 chia het cho 31 ( dpcm ) 

Answer 2

Ta có: \(2^{1995}=\left(2^5\right)^{399}=32^{399}⋮32\)

Mà \(32\equiv1\)(mod 31)

\(\Rightarrow2^{1995}\equiv1\)(mod 31)

\(\Rightarrow2^{1995}-1⋮31\)(đpcm)

           

Answer 3

Ta có : \(2^{1995}=2^{1990}\cdot2^5=2^{1990}\cdot32\)

Vì \(32\div31\)dư 1 \(\Rightarrow32\cdot2^{1990}⋮31\)

vạy \(2^{1995}-1⋮31\)