Prove that the square of any positive integer is of the form `5q ,5q+1,5q+4` for some integer `qdot`

Explanation

To prove that the square of any positive integer is of the form \(5q\), \(5q + 1\), or \(5q + 4\) for some integer \(q\), we will consider all possible cases for a positive integer \(x\) based on its remainder when divided by 5.

### Step 1: Consider the possible forms of \(x\)
A positive integer \(x\) can be expressed in one of the following forms based on its remainder when divided by 5:
1. \(x = 5q\)
2. \(x = 5q + 1\)
3. \(x = 5q + 2\)
4. \(x = 5q + 3\)
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