If `z_(1)and z_(2)` are two distinct complex numbers satisfying the relation `|z_(1)^(2)-z_(2)^(2)|=|barz_(1)^(2)+barz_(2)^(2)-2barz_(1)barz_(2)| and (argz_(1)-argz_(2))=(api)/(b)`, then the least possible value of `|a-b|` is equal to (where, a & b are integers)

Answer

To solve the problem, we need to analyze the given equation and the conditions provided.

### Step-by-Step Solution:

1. **Understanding the Given Condition:**
We start with the equation:
\[ |z_1^2 - z_2^2| = |\overline{z_1^2} + \overline{z_2^2} - 2\overline{z_1}\overline{z_2}| \]
We can rewrite \(z_1^2 - z_2^2\) as \((z_1 - z_2)(z_1 + z_2)\).

2. **Rewriting the Right Side:**
The right-hand side can be simplified using the properties of conjugates:
\[ \overline{z_1^2} = \overline{z_1}^2 \quad \text{and} \quad \overline{z_2^2} = \overline{z_2}^2 \]
Thus, we have:
\[ |\overline{z_1}^2 + \overline{z_2}^2 - 2\overline{z_1}\overline{z_2}| = |(\overline{z_1} - \overline{z_2})^2| \]
This can be expressed as:
\[ |z_1 - z_2|^2 \]

3. **Setting Up the Equation:**
Now we have:
\[ |(z_1 - z_2)(z_1 + z_2)| = |(\overline{z_1} - \overline{z_2})^2| \]
This implies:
\[ |z_1 - z_2| |z_1 + z_2| = |z_1 - z_2|^2 \]
Since \(z_1\) and \(z_2\) are distinct, we can divide both sides by \(|z_1 - z_2|\):
\[ |z_1 + z_2| = |z_1 - z_2| \]

4. **Geometric Interpretation:**
The equation \(|z_1 + z_2| = |z_1 - z_2|\) indicates that the points \(z_1\) and \(z_2\) are equidistant from the origin. This means that the line joining \(z_1\) and \(z_2\) is perpendicular to the line joining \(z_1 + z_2\) to the origin.

5. **Using Argument Condition:**
We also know that:
\[ \arg(z_1) - \arg(z_2) = \frac{\pi}{b} \]
This implies that the angle between the two complex numbers is a rational multiple of \(\pi\).

6. **Finding Values of \(a\) and \(b\):**
From the geometric interpretation, we can deduce that:
\[ \arg\left(\frac{z_1}{z_2}\right) = \frac{\pi}{2} \]
This means:
\[ \arg(z_1) - \arg(z_2) = \frac{\pi}{2} \]
Thus, we can set \(a = 1\) and \(b = 2\).

7. **Calculating \(|a - b|\):**
Finally, we need to find:
\[ |a - b| = |1 - 2| = 1 \]

### Final Answer:
The least possible value of \(|a - b|\) is:
\[ \boxed{1} \]