Polynomial Whose Values at the Integers are n-th Power of Integers in a Quadratic Field

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Published: Jan 5, 2018
Keywords:
integer-valued polynomial, quadratic integer.

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Janyarak Tongsomporn*
School of Science, Walailak University, Nakhon Si Thammarat, Thailand
Vichian Laohakosol
Department of Mathematics, Faculty of Science, Kasetsart University, Bangkok, Thailand

Abstract

Let f(x1,x2,...,xk) gif.latex?\in gif.latex?\kappa [x1,x2,...,xk], where gif.latex?\kappa  is a quadratic field. We investigate the polynomial f (x1,x2,...,xk) which becomes always an nth power of an quadratic integer using the technique of Kojima. It is shown that if f (gif.latex?\alpha1,gif.latex?\alpha2,...gif.latex?\alphak) is an nth power of an element in Ok , the ring of integers of gif.latex?\kappa, then f (x1,x2,...,xk)=(gif.latex?\varnothing(x1,x2,...xk))n,for somegif.latex?\varnothing (x1,x2,...,xk) gif.latex?\inOk [x1,x2,...xk].


Keywords: integer-valued polynomial, quadratic integer.


*Corresponding author:       E-mail: janyarak.to@wu.ac.th

Article Details

How to Cite
Tongsomporn*, J., & Laohakosol, V. (2018). Polynomial Whose Values at the Integers are n-th Power of Integers in a Quadratic Field. CURRENT APPLIED SCIENCE AND TECHNOLOGY, 17(1), 13–21. retrieved from https://li01.tci-thaijo.org/index.php/cast/article/view/128639
Issue
Vol. 17 No. 1 (2017)
Section
Original Research Articles

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References

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