Question

chứng minh rằng 5⁵-5⁴⁺5³ chia hết cho 7

Answer 1

ta có : \(5^5-5^4+5^3=5^3\left(5^2-5+1\right)=5^3.21=5^3.3.7⋮7\)

\(\Rightarrowđpcm\)

Answer 2

\(5^5-5^4+5^3=5^3\left(5^2-5+1\right)=5^3\cdot\left(25-5+1\right)=5^3\cdot21\)

Vì \(21⋮7\Rightarrow5^3\cdot21⋮7\Rightarrow5^5-5^4+5^3⋮7\)

Vậy \(5^5-5^4+5^3⋮7\left(đpcm\right)\)