id: 06619343
dt: j
an: 2016e.00781
au: Aabrandt, Andreas; Hansen, Vagn Lundsgaard
ti: A note on powers in finite fields.
so: Int. J. Math. Educ. Sci. Technol. 47, No. 6, 987-991 (2016).
py: 2016
pu: Taylor \& Francis, Abingdon, Oxfordshire
la: EN
cc: H40 F60
ut: finite fields; prime numbers; squares and powers in finite fields
ci:
li: doi:10.1080/0020739X.2015.1129076
ab: Summary: The study of solutions to polynomial equations over finite fields
has a long history in mathematics and is an interesting area of
contemporary research. In recent years, the subject has found important
applications in the modelling of problems from applied mathematical
fields such as signal analysis, system theory, coding theory and
cryptology. In this connection, it is of interest to know criteria for
the existence of squares and other powers in arbitrary finite fields.
Making good use of polynomial division in polynomial rings over finite
fields, we have examined a classical criterion of Euler for squares in
odd prime fields, giving it a formulation that is apt for
generalization to arbitrary finite fields and powers. Our proof uses
algebra rather than classical number theory, which makes it convenient
when presenting basic methods of applied algebra in the classroom.
rv: