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One can use the number theoretic idea of the notion of natural density\cite{B1} to define topological s-torsion elements (which form thestatistically characterized subgroups, recently developed in \cite{DPK})extending Armacost's idea of topological torsion elements. We follow in theline of Armacost who had posed the famous classical problem for "description oftopological torsion elements" of the circle group. In this note we consider thenatural density version of Armacost's problem and present a completedescription of topological s-torsion elements in terms of the support, for allarithmetic sequences which also provides the solution of Problem 6.10 posed in\cite{DPK} .

Topological torsion elements via natural density and a quest for solution of Armacost like problem