Q:

Proof problem: If $x-1$ is divisible by $4$ then $x^2 - 1$ is divisible by 4

The question is to state if it's true or false.
Question: If $x-1$ is divisible by 4 then $x^2 - 1$ is divisible by 4
I'm not very familiar with the mathematical language of elementary number theory compared to calculus, algebra as this is mostly calculations and using the correct properties. It would be great if you can show me steps to understand. 

A:

$x^2-1=(x-1)(x+1)$ this implies the result.

A:

If $x−1$ is divisible by $4$ then $\,x -1 = 4n\,$ for some integer $n\,$. Then $\,x^2-1$ $=(4n+1)^2-1$ $\require{cancel}=16n^2 + 8n + \cancel{1} - \cancel{1} = 8n(2n+1)\,$ is divisible by $8$, which is in turn divisible by $4$.

