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

Options

A. `m`
B. `m+1`
C. `2m`
D. `2m+1`

Explanation

To show that every even integer can be expressed in the form of \(2m\) for some integer \(m\), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Even Integers**:
An even integer is defined as any integer that is divisible by 2. This means that when you divide an even integer by 2, there is no remainder.

2. **General Form of Even Integers**:
We can express any even integer mathematically. If we take an integer \(m\), then multiplying \(m\) by 2 gives us an even integer. Thus, we can write:
\[ \text{Even Integer} = 2m \]
where \(m\) is any integer.

3. **Examples of Even Integers**:
Let's consider some examples:
- If \(m = 0\), then \(2m = 2 \times 0 = 0\) (which is even).
- If \(m = 1\), then \(2m = 2 \times 1 = 2\) (which is even).
- If \(m = 2\), then \(2m = 2 \times 2 = 4\) (which is even).
- If \(m = -1\), then \(2m = 2 \times -1 = -2\) (which is even).
- If \(m = -2\), then \(2m = 2 \times -2 = -4\) (which is even).

4. **Conclusion**:
Since we can find an integer \(m\) for every even integer, we conclude that every even integer can indeed be expressed in the form \(2m\).

### Final Statement:
Therefore, every even integer is of the form \(2m\) for some integer \(m\).

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