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Recently, L. Block has shown that for any mapping / of an interval, whether / has a periodic point whose period contains an odd factor greater than 1 depends entirely on the periodic orbits of / whose periods are powers of 2. In this paper the author shows that Block's result is a special case of a more general phenomenon.doi:10.2307/2000088 fatcat:kqjikvncwva5thwni7ikgbep7m