Find all positive integers $n$ which satisfy the following tow conditions:
(a) $n$ has at least four different positive divisors;
(b) for any divisors $a$ and $b$ of $n$ satisfying $1<a<b<n$, the number $b-a$ divides $n$.

[i](4th Middle European Mathematical Olympiad, Individual Competition, Problem 4)[/i]
To find all positive integers \( n \) that satisfy the given conditions, we will analyze the problem step by step.

1. **Condition (a): \( n \) has at least four different positive divisors.**

   This implies that \( n \) cannot be a prime number or the square of a prime number, as these have fewer than four divisors. Therefore, \( n \) must be either a product of two distinct primes, a cube of a prime, or a higher power of a prime.

2. **Condition (b): For any divisors \( a \) and \( b \) of \( n \) satisfying \( 1 < a < b < n \), the number \( b - a \) divides \( n \).**

   We will consider different forms of \( n \) and check if they satisfy both conditions.

3. **Case 1: \( n \) is a product of two distinct primes, \( n = p_1 p_2 \).**

   - If \( n = p_1 p_2 \), the divisors of \( n \) are \( 1, p_1, p_2, \) and \( n \).
   - For \( n \) to have at least four divisors, \( p_1 \) and \( p_2 \) must be distinct primes.
   - Check if \( b - a \) divides \( n \) for all \( 1 < a < b < n \).

4. **Case 2: \( n \) is a cube of a prime, \( n = p^3 \).**

   - If \( n = p^3 \), the divisors of \( n \) are \( 1, p, p^2, \) and \( p^3 \).
   - Check if \( b - a \) divides \( n \) for all \( 1 < a < b < n \).

5. **Case 3: \( n \) is a higher power of a prime, \( n = p^k \) for \( k \geq 4 \).**

   - If \( n = p^k \), the divisors of \( n \) are \( 1, p, p^2, \ldots, p^k \).
   - Check if \( b - a \) divides \( n \) for all \( 1 < a < b < n \).

6. **Analysis of specific values:**

   - **\( n = 6 \):**
     - Divisors: \( 1, 2, 3, 6 \).
     - Check \( b - a \) for \( 1 < a < b < 6 \):
       - \( b = 3, a = 2 \Rightarrow b - a = 1 \), which divides \( 6 \).
     - Satisfies both conditions.

   - **\( n = 8 \):**
     - Divisors: \( 1, 2, 4, 8 \).
     - Check \( b - a \) for \( 1 < a < b < 8 \):
       - \( b = 4, a = 2 \Rightarrow b - a = 2 \), which divides \( 8 \).
     - Satisfies both conditions.

   - **\( n = 12 \):**
     - Divisors: \( 1, 2, 3, 4, 6, 12 \).
     - Check \( b - a \) for \( 1 < a < b < 12 \):
       - \( b = 4, a = 2 \Rightarrow b - a = 2 \), which divides \( 12 \).
       - \( b = 6, a = 2 \Rightarrow b - a = 4 \), which divides \( 12 \).
       - \( b = 6, a = 3 \Rightarrow b - a = 3 \), which divides \( 12 \).
     - Satisfies both conditions.

7. **Conclusion:**

   The integers \( n \) that satisfy both conditions are \( 6, 8, \) and \( 12 \).

The final answer is \( \boxed{6, 8, 12} \).