  The old "glue--and--cut" symmetry of massless propagators, first established
in [1], leads --- after reduction to master integrals is performed --- to a
host of non-trivial relations between the latter. The relations constrain the
master integrals so tightly that they all can be analytically expressed in
terms of only few, essentially trivial, watermelon-like integrals. As a
consequence we arrive at explicit analytical results for all master integrals
appearing in the process of reduction of massless propagators at three and four
loops. The transcendental structure of the results suggests a clean explanation
of the well-known mystery of the absence of even zetas (zeta_{2n}) in the Adler
function and other similar functions essentially reducible to the massless
propagators. Once a reduction of massless propagators at five loops is
available, our approach should be also applicable for explicit performing the
corresponding five-loop master integrals.
