Câu hỏi của Nguyễn Quỳnh Mai

Question

Chứng minh:

4^2018 - 1 chia hết cho 3

5^2019 - 1 chia hết cho 4

4^2019 + 1 chia hết cho 5

5^2017 + 1 chia hết cho 6

giúp mk với nha mn

Nguyễn Huy Tú · Accepted Answer

a, Ta có: $4\equiv1\left(mod3\right)$

$\Rightarrow4^{2018}\equiv1\left(mod3\right)$

$\Rightarrow4^{2018}-1⋮3$

b, Ta có: $5\equiv1\left(mod4\right)$

$\Rightarrow5^{2019}\equiv1\left(mod4\right)$

$\Rightarrow5^{2019}-1⋮4$

c, $4\equiv-1\left(mod5\right)$

$\Rightarrow4^{2019}\equiv-1\left(mod5\right)$

$\Rightarrow4^{2019}+1⋮5$

d, $5\equiv-1\left(mod6\right)$

$\Rightarrow5^{2017}\equiv-1\left(mod6\right)$

$\Rightarrow5^{2017}+1⋮6$Câu trả lời: a, Ta có: $4\equiv1\left(mod3\right)$

$\Rightarrow4^{2018}\equiv1\left(mod3\right)$

$\Rightarrow4^{2018}-1⋮3$

b, Ta có: $5\equiv1\left(mod4\right)$

$\Rightarrow5^{2019}\equiv1\left(mod4\right)$

$\Rightarrow5^{2019}-1⋮4$

c, $4\equiv-1\left(mod5\right)$

$\Rightarrow4^{2019}\equiv-1\left(mod5\right)$

$\Rightarrow4^{2019}+1⋮5$

d, $5\equiv-1\left(mod6\right)$

$\Rightarrow5^{2017}\equiv-1\left(mod6\right)$

$\Rightarrow5^{2017}+1⋮6$

Phương Trâm · Answer

1. Vì $4$ chia $3$ dư $1$

$\Rightarrow4^{2018}$ chia $3$ dư $1^{2018}=1.$

$\Rightarrow4^{2018}-1$ chia hết cho $3.$Câu trả lời: 1. Vì $4$ chia $3$ dư $1$

$\Rightarrow4^{2018}$ chia $3$ dư $1^{2018}=1.$

$\Rightarrow4^{2018}-1$ chia hết cho $3.$