Question

[Luna]

Tìm số dư của phép chia sau :

a) \(3^{100}:7\)           b) \(9!:11\)                        c) \(\left(2^{100}+3^{105}\right):15\)                           d) ( \(1532^5-1\)) :9

Answer 1

[Trần Minh Đăng]

a) du 4

b)du 6

c) du 1

d)  connect failed - wait...

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Answer 2

[Shiba Inu]

${\mathrm{a)\; 3}}^6\equiv 1\left(mod7\right)$

${\left(3^6\right)}^{16}\equiv 1\left(mod7\right)$

$3^2\equiv 2\left(mod7\right)$

${\left(3^2\right)}^2\equiv 2^2\left(mod7\right)$

$3^4\equiv 4\left(mod7\right)$

Suy ra ${\left(3^6\right)}^{16}{.3}^4\equiv 4\left(mod7\right)$

Vậy 3100 chia 7 dư 4