In a recent investigation of dihedral quartic fields  a rational sequence (a n ) was encountered. We show that these a n 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 , where the corresponding p-adic numbers are known completely . Other unsolved problems are presented. The growth of the a n is examined and a new algorithm for computing a n is given. An appendix by D. Zagicr, which carries the investigation further, is added.
KeywordsModular Form Eisenstein Series Modular Function Modular Group Algebraic Integer
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