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

Options

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

Explanation

To solve the problem of expressing every even integer 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, you get another integer.

2. **General Form of Even Integers**:
- The general form of an even integer can be expressed as \(2n\), where \(n\) is any integer. This is because multiplying any integer \(n\) by 2 will yield an even integer.

3. **Substituting \(n\) with \(m\)**:
- In the context of the problem, we can let \(m\) be equal to \(n\). Therefore, we can rewrite the expression for even integers as \(2m\), where \(m\) is any integer.

4. **Conclusion**:
- Thus, we conclude that every even integer can be expressed in the form \(2m\) for some integer \(m\).

### Final Expression:
- Therefore, every even integer is of the form \(2m\), where \(m\) is an integer.