Sequences Generated by Polynomials over Integral Domains
DOI:
https://doi.org/10.48048/wjst.2019.6957Keywords:
Polynomial sequences, sequence over integral domain, interpolation polynomialsAbstract
Let D be an integral domain. For sequences a = (a1; a2; : : : ; an) and I = (i1; i2; : : : ; in) in Dn with distinct ij , call a a (Dn; I)-polynomial sequence if there exists f(x) 2 D[x] such that f(ij) = aj (j =1; : : : ; n). Criteria for a sequence to be a (Dn; I)-polynomial sequence are established and explicit structures of Dn/Pn;I where Pn;I is the set of all (Dn; I)-polynomial sequences are determined.Downloads
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EF Cornelius Jr and P Schultz. Sequences generated by polynomials. Amer. Math. Monthly 2008; 115, 154-8.
PJ Davis. Interpolation and Approximation. Dover, New York, 1975.
I Stewart and D Tall. Algebraic Number Theory and Fermat’s Last Theorem. CRC Press, 2001.
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