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In this paper we introduce a transformation group connected with Poncelet's porism. Several open questions following from our considerations end the paper. The aim of this paper is to give a new approach to find an algebraic Fuss-type formula for all natural n>2. Developed method may be applied to investigations of Poncelet's porism.

This paper deals with infinite binary sequences. Each sequence is treated as generated by a nondeterministic shift register. A measure-theoretic criterion helpful in finding a deterministic generator of the set of sequences is proposed.

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