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There are Only Eleven Special Pisot Numbers

Authors:	Smyth C J

Institution:	Department of Mathematics and Statistics, The University of Edinburgh James Clerk Maxwell Building, King's Buildings, Mayfield Road, Edinburgh EH9 3JZ

Abstract:	A special Pisot number is a Pisot number ${alpha}$ such that ${alpha}$ /( ${alpha}$ –1)is also a Pisot number. Lagarias, Porta and Stolarsky found11 special Pisot numbers. Here it is proved that there are nomore. Also, the one known Salem number ${tau}$ with the property that ${tau}$ /( ${tau}$ –1) is a Pisot number is shown to be the only such number.1991 Mathematics Subject Classification 11R06.

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