For some integer q, every odd integer is of the form

To prove that every odd integer is of the form q, we can follow these steps:

Step 1: Let's consider an arbitrary odd integer, which we can represent as 2k + 1, where k is an integer.

Step 2: We need to show that this odd integer can be written in the form q, where q is some integer.

Step 3: By substituting 2k + 1 for q in the equation, we have q = 2k + 1.

Step 4: Since k is an integer, 2k is also an integer. Adding 1 to 2k gives us an odd integer.

Step 5: Therefore, we have shown that every odd integer can be expressed in the form q, where q is an integer.

In conclusion, every odd integer is of the form q, where q is some integer.