Nếu $n$ chia hết cho $3$ thì $n=3k$ với $k\in \mathbb{N}$.

 Xét $k=2m$ thì $n=6m$ suy ra $n(n+1)=6m(6m+1)$ chia hết cho $6$.

 Xét $k=2m+1$ thì $n=3(2m+1)=6m+3$.

Suy ra $n(n+1)=(6m+3)(6m+4)=3.(2m+1).2(3m+2)=6.(2m+1).(3m+2)$ chia hết cho $6$.

Vậy với mọi số tự nhiên $n$, nếu $n$ chia hết cho $3$ thì $n(n+1)$ chia hết cho $6$.

Nếu $n$ lẻ thì $n$ có dạng $n=2k+1$ với $k\in \mathbb{N}$.

Do đó $n^3=(2k+1{)}^3=8k^3+12k^2+6k+1=2(4k^3+6k^2+3k)+1$.

Suy ra $n^3$ lẻ.

Vậy với mọi số tự nhiên $n$, nếu $n$ lẻ thì $n^3$ lẻ.

- It's a hand

- It's an eraser

- No, it isn't

- It's blue

- They're red

My name's Mai. I'm thirty years old. I'm fine today. My hobby is travelling. I have a green pencil.

1. I'm thirty years old

2. My hobby is cooking

3. Yes, i do

4. I learn English at break time

1. No, I don't

2. I play word puzzles

3. It's blue

4. My hobby is badminton

1. My father name's Dai

2. My hobbies are travelling, cooking, dancing, and singing

3. Yes, I can

4. My father name's Dai

5. Her hobby is cooking

1. That's an eye

2. She's three years old

3. Her hobby is cooking

4. His hobby is running

5. No, it isn't. It's Ben

1. My name's Mai

2. I'm thirty years old

3. My hobbies are shopping, travelling, cooking and dancing

4. Her hobby is cooking

1. It's an ear

2. She's 6 years old

3. Yes, it is

4. It's singing