Abstract
I study here the arithmetical properties of the four polynomials An, Bn, C., and Dn associated with the real multiplication of Jacobi's sn, cn, and dn.2 Here each of Ann , Dn is a polynomial in sn2u and 72 with rational integral coefficients. Consequently, if we substitute for sn2u and 72 two fixed algebraic numbers, we obtain four sequences of algebraic numbers (A), (B), (C) and (D). The arithmetical properties of these elliptic sequences are the subject of this investigation. If 72 is zero or one, the four sequences reduce essentially to Lucas' sequences (U) and (1V), where Vl7 = an + 13n.
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