  We consider an example of the joint system of dynamical differential
equations and qKZ difference equations with parameters corresponding to
equations for elliptic integrals. We solve this system of equations modulo any
power $p^n$ of a prime integer $p$. We show that the $p$-adic limit of these
solutions as $n\to\infty$ determines a sequence of line bundles, each of which
is invariant with respect to the corresponding dynamical connection, and that
sequence of line bundles is invariant with respect to the corresponding qKZ
difference connection.
