Sequences Generated by Polynomials over Integral Domains

Veasna KIM; Vichian LAOHAKOSOL; Supawadee PRUGSAPITAK

doi:10.48048/wjst.2019.6957

Sequences Generated by Polynomials over Integral Domains

Authors

Veasna KIM Department of Mathematics and Statistics, Prince of Songkla University, Songkhla 90110
Vichian LAOHAKOSOL Department of Mathematics, Kasetsart University, Bangkok 10900
Supawadee PRUGSAPITAK Department of Mathematics and Statistics, Prince of Songkla University, Songkhla 90110

DOI:

https://doi.org/10.48048/wjst.2019.6957

Keywords:

Polynomial sequences, sequence over integral domain, interpolation polynomials

Abstract

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.

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References

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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Published

2019-05-29

How to Cite

KIM, V., LAOHAKOSOL, V., & PRUGSAPITAK, S. (2019). Sequences Generated by Polynomials over Integral Domains. Walailak Journal of Science and Technology (WJST), 16(9), 625–633. https://doi.org/10.48048/wjst.2019.6957