Show that cube of any positive integer is of the form 4m, 4m+1 or 4m+3, for some integer m.

Explanation

To show that the cube of any positive integer is of the form \(4m\), \(4m + 1\), or \(4m + 3\) for some integer \(m\), we can follow these steps:

### Step 1: Consider a positive integer \(a\)
Let \(a\) be any positive integer.

### Step 2: Use the Division Algorithm
According to the division algorithm, we can express \(a\) in the form:
\[
...