Question

Tìm số dư khi 3^100 chia cho 4.

Answer 1

3¹⁰⁰ = 3⁴.3⁹⁶

3⁴= 1( mod 4 )

3⁹⁶=( 3³)³²

3³= -1 ( mod 4)

=> 3⁹⁶ = 1 (mod 4)

=> 3¹⁰⁰= 1 (mod 4)

3¹⁰⁰ chia 4 dư 1

Answer 2

\(3^2\equiv1\left(\text{mod }4\right)\)

\(\Leftrightarrow\left(3^2\right)^{50}\equiv1\left(\text{mod }4\right)\)

\(\Leftrightarrow3^{100}-1⋮4\)

\(\Leftrightarrow3^{100}\text{ chia }4\text{ dư }1\)

Answer 3

Có \(3\equiv-1\left(mod4\right)\Rightarrow3^{100}\equiv1\left(mod4\right)\)

Vậy..