For some integer m, every even integer is of the form

To prove that every even integer is of the form "m", we can follow these steps:

Step 1: Let's consider an arbitrary even integer "n".

Step 2: By definition, an even integer can be expressed as "n = 2k", where "k" is an integer.

Step 3: Now, let's define "m" as "m = k".

Step 4: Substituting "k" in the expression for "n", we have "n = 2m".

Step 5: Therefore, we have shown that every even integer "n" can be expressed in the form "m", where "m" is an integer.

Step 6: Since we have proven this for an arbitrary even integer, we can conclude that every even integer is of the form "m".

Thus, we have successfully demonstrated that every even integer is of the form "m".