Journal of Prime Research in Mathematics

# On existence of canonical number system in certain classes of pure algebraic number fields

Abdul Hameed
National University of Computer & Emerging Sciences, Lahore Campus, Lahore, Pakistan.
Toru Nakahara
National University of Computer & Emerging Sciences, Peshawar Campus, Peshawar, Pakistan.
$$^{1}$$Corresponding Author: abdul.hameed@lhr.nu.edu.pk
Canonical Number System can be considered as natural generalization of radix representation of rational integers to algebraic integers. We determine the existence of Canonical Number System in two classes of pure algebraic number fields of degree $$2^n$$ and $$n$$.