Polynomial Whose Values at the Integers are n-th Power of Integers in a Quadratic Field
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Abstract
Let f(x1,x2,...,xk)
[x1,x2,...,xk], where
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 (
1,
2,...
k) is an nth power of an element in Ok , the ring of integers of
, then f (x1,x2,...,xk)=(
(x1,x2,...xk))n,for some
(x1,x2,...,xk)
Ok [x1,x2,...xk].
Keywords: integer-valued polynomial, quadratic integer.
*Corresponding author: E-mail: janyarak.to@wu.ac.th
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