Question

[Anh Đỗ Ngọc]

CMR a mũ 2 -a chia hết cho 2 (a thuộc N)

Answer 1

[Yuri Sweet[𝕿𝖊𝖆𝖒 𝕹𝖊𝖕𝖆𝖑]]

Ta có : \(a^2-a=a\left(a-1\right)\)

Xét :

• \(a=2k\left(k\inℕ\right)\)

\(\Rightarrow a\left(a-1\right)=2k\left(2k-1\right)⋮2\)

• \(a=2k+1\left(k\inℕ\right)\)

\(\Rightarrow a\left(a-1\right)=\left(2k+1\right)\left(2k+1-1\right)=\left(2k+1\right)2k⋮2\)

Suy ra : \(a\left(a-1\right)⋮2\forall a\inℕ\)

hay \(a^2-a⋮2\forall a\inℕ\)