Proof that if n is divisible by 7 then n² is divisible by 7

Let $n$ be an integer that is divisible by 7.

By the definition of divisibility, if $n$ is divisible by 7, then $n$ can be written in the form $n = 7k$ for some integer $k$.

Now, let's look at n²:
n² = (7k)²

n² = 7² * k²
n² = 49k²

n² = 7 * (7k²)

Let m = 7k². Since $k$ is an integer, k² is an integer, and therefore 7k² is also an integer.
So, n² = 7m, where $m$ is an integer.
By the definition of divisibility, this means n² is divisible by 7.

Therefore, if $n$ is divisible by 7, then n² is divisible by 7.