The contact force applied by a body A on another body B is equal to...

The contact force $F_{c}$ between two bodies is the resultant of the normal force $N$ and the frictional force $f$.

$F_{c} = \sqrt{N^2 + f^2}$

Given that the contact force is equal to the normal force, we have $F_{c} = N$.

$\sqrt{N^2 + f^2} = N$

$N^2 + f^2 = N^2$

$f = 0$

Thus, the frictional force between the bodies is zero.

The frictional force can be zero if the surfaces are frictionless, or if the surfaces are rough but there is no tendency of relative motion between them. If the surfaces are rough and the frictional force is zero, the bodies do not slip on each other.

Therefore, the frictional force is zero, and the bodies may be rough but they do not slip on each other.