For integers m and n, both greater than 1, consider the following three statements
P : m divides n, Q : m divides `n^(2)` , R : m is prime then

Options

A. `Q ^^ R rarr P`
B. `P ^^ Q rarr R`
C. `Q rarr R`
D. `Q rarr P`

Answer

To solve the problem, we need to analyze the relationships between the statements P, Q, and R given the conditions of integers \( m \) and \( n \) both greater than 1.

### Step-by-step Solution:

1. **Understanding the Statements:**
- Statement P: \( m \) divides \( n \) (denoted as \( m \mid n \)).
- Statement Q: \( m \) divides \( n^2 \) (denoted as \( m \mid n^2 \)).
- Statement R: \( m \) is a prime number.

2. **Analyzing the Implications:**
- If \( m \mid n \) (P is true), then \( n \) can be expressed as \( n = km \) for some integer \( k \).
- Squaring \( n \), we get \( n^2 = (km)^2 = k^2m^2 \).
- Since \( n^2 \) is a multiple of \( m^2 \), it follows that \( m \mid n^2 \) (Q is true) because \( m \) divides \( k^2m^2 \).

3. **Conclusion from P to Q:**
- Therefore, if P is true, Q must also be true. This establishes that P implies Q.

4. **Considering Statement R:**
- Statement R states that \( m \) is a prime number. The truth of R does not affect the truth of P or Q directly.
- However, if \( m \) is prime, it does not necessarily imply anything about the relationship between P and Q.

5. **Final Relationships:**
- We conclude that:
- Q is related to P (if P is true, Q is true).
- The truth of R does not affect the relationship between P and Q.

### Answer:
The correct option is that Q and R are related to P.