Polynomial Whose Values at the Integers are n-th Power of Integers in a Quadratic Field - Tongsomporn*, Janyarak; Laohakosol, Vichian (CURRENT APPLIED SCIENCE AND TECHNOLOGY, 2018)
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