Question

chứng minh 5¹⁰⁰ + 5⁹⁸ chia hết cho 13

Answer 1

\(5^{100}+5^{98}=5^{98}\left(5^2+1\right)=5^{98}.26\)

Vì \(26⋮13\) nên \(5^{100}+5^{98}⋮13\)

Answer 2

Ta có:

\(5^{100}+5^{98}=5^{98}.\left(5^2+1\right)=5^{98}.\left(25+1\right)=5^{98}.26\)

Vì \(26⋮13\Rightarrow5^{98}.26⋮13\Rightarrow5^{100}+5^{98}⋮13\)