Question

CTR tích \(13^n.\left(13^n+3\right).\left(13^n+4\right).\left(13^n+1\right)⋮4\)với \(n\inℕ\)

Answer 1

\(Tacó\)

\(13\equiv1\left(mod4\right)\Rightarrow13^n\equiv1\left(mod4\right)\)

\(\Rightarrow\left(13^n+3\right)⋮4\Leftrightarrow13^n\left(13^n+3\right)\left(13^n+4\right)\left(13^n+1\right)⋮4\left(đpcm\right)\)

Answer 2

Vì n \(\in\) N nên 13ⁿ lẻ \(\Rightarrow\) 13ⁿ + 3 và 13ⁿ + 1 đều chẵn \(\Rightarrow\) (13ⁿ + 3) . (13ⁿ + 1) \(⋮\) 4 \(\Rightarrow\) 13ⁿ . (13ⁿ + 3) . (13ⁿ + 4) . (13ⁿ + 1) \(⋮\) 4