On a Sequence Arising in Series for it
نویسندگان
چکیده
In a recent investigation of dihedral quartic fields [6] a rational sequence {a„} was encountered. We show that these a„ are positive integers and that they satisfy surprising congruences modulo a prime p. They generate unknown p-adic numbers and may therefore be compared with the cubic recurrences in [1], where the corresponding ^-adic numbers are known completely [2]. Other unsolved problems are presented. The growth of the a„ is examined and a new algorithm for computing a„ is given. An appendix by D. Zagier, which carries the investigation further, is added.
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تاریخ انتشار 2010