Question

CMR: 
a, 5⁵ - 5⁴ + 5³ ⋮ 7
b, 7⁶ + 7⁵ - 7⁴ ⋮ 11
c, 10⁹ + 10⁸ + 10⁷ ⋮ 222

Answer 1

a) \(5^5-5^4+5^3=5^3\left(25-5+1\right)=5^3.21=5^3.3.7⋮7\)

b) \(7^6+7^5-7^4=7^4\left(7^2+7-1\right)=7^4.55=7^4.5.11⋮11\)

c) \(10^9+10^8+10^7=10^6\left(10^3+10^2+10\right)=10^6.1110=10^6.5.222⋮222\)

Answer 2

a) 5⁵ - 5⁴ + 5³ = 5³.(5² - 5 + 1) = 5³.21 ⋮ 7 (do 21 ⋮ 7)

b) 7⁶ + 7⁵ - 7⁴ = 7⁴.(7² + 7 - 1) = 7⁴.55 ⋮ 11 (do 55 ⋮ 11)

c) 10⁹ + 10⁸ + 10⁷ = 10⁷.(10² + 10 + 1) = 10⁷.111 = 2⁷.5⁷.111 - 2⁶.5⁷.222 ⋮ 222

Answer 3

haha