When finding the maximum margin separator in the primal form we have the quadratic program:

$$min\frac{1}{2}||\theta||^2$$ $$\text{ subject to: } y^{(t)}(\theta \cdot x^{(t)} + \theta_0) \geq 1, \ t=1,...,n$$

Saying basically to find the maximum margin separator. The margin size will be:

$$\frac{1}{||\theta||}$$

does the size of the margin change whether we change the constant of the constraints?

i.e. if we have:

$$\text{ subject to: } y^{(t)}(\theta \cdot x^{(t)} + \theta_0) \geq k, \ t=1,...,n$$

instead of 1?

If it does not matter, why doesn't this matter? How is it an equivalent formulation regardless of the exact constant for the constraint?