Let $a, b, c$ be pairwise coprime natural numbers. A positive integer $n$ is said to be [i]stubborn[/i] if it cannot be written in the form 
$n = bcx+cay+abz$, for some $x, y, z \in\mathbb{ N}.$ Determine the number of stubborn numbers.
To determine the number of stubborn numbers, we need to analyze the given problem in detail. We are given that \(a, b, c\) are pairwise coprime natural numbers, and a positive integer \(n\) is said to be stubborn if it cannot be written in the form \(n = bcx + cay + abz\) for some \(x, y, z \in \mathbb{N}\).

1. **Understanding the Form \(n = bcx + cay + abz\)**:
   - Since \(a, b, c\) are pairwise coprime, the form \(n = bcx + cay + abz\) represents a linear combination of \(bc, ca, ab\) with coefficients in \(\mathbb{N}\).
   - This form is similar to the Frobenius coin problem but in three dimensions.

2. **Largest Non-Stubborn Number**:
   - From the Frobenius coin problem in two dimensions, we know that the largest number that cannot be expressed as \(bx + cy\) for \(x, y \in \mathbb{N}\) is \(bc - b - c\).
   - Extending this to three dimensions, the largest number that cannot be expressed as \(bcx + cay + abz\) is \(2abc - ab - bc - ca\).

3. **Counting Stubborn Numbers**:
   - We need to count the positive integers in the interval \([1, 2abc]\) that can be written in the form \(bcx + cay + abz\).
   - The number of non-stubborn numbers is given by the number of integers that can be written in the form \(bcx + cay + abz\) within the interval \([1, 2abc]\).

4. **Using the Inclusion-Exclusion Principle**:
   - We need to count the number of integers that can be written as \(bcx + cay + abz\) and subtract this from the total number of integers in the interval \([1, 2abc]\).
   - The total number of integers in the interval \([1, 2abc]\) is \(2abc\).

5. **Conclusion**:
   - The number of stubborn numbers is the total number of integers in the interval \([1, 2abc]\) minus the number of integers that can be written in the form \(bcx + cay + abz\).
   - Since \(2abc\) is the largest non-stubborn number, all numbers from \(1\) to \(2abc\) can be written in the form \(bcx + cay + abz\) except for the stubborn numbers.

Therefore, the number of stubborn numbers is given by:
\[
\boxed{abc - ab - bc - ca}
\]