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We study the properties of roots of a polynomial system of equations whichdefine a set of identical point particles located on a Unique Worldline (UW),in the spirit of the old Wheeler-Feynman's conception. As a consequence of theVieta's formulas, a great number of conservation laws is fulfilled forcollective algebraic dynamics on the UW. These, besides the canonical ones,include the laws with higher derivatives and those containing multi-particlecorrelation terms as well. On the other hand, such a ``super-conservative''dynamics turns to be manifestly Lorentz invariant and quite nontrivial. Atgreat values of ``cosmic time'' $t$ roots-particles demonstrate universalrecession (resembling that in the Milne's cosmology and simulating``expansion'' of the Universe) for which the Hubble's law does hold true, withHubble parameter being inversely proportional to $t$.

The algebrodynamics: super-conservative collective dynamics on a "Unique Worldline'' and the Hubble's law