Let
be a prime
number and set
.
A
-sequence is
a function
.
Let
be
the set
.
We prove that the set of sequences of the form
, where
, is precisely the set of
periodic
-sequences with
period equal to a
-power.
Given a
-sequence, we
will also determine all
that correspond to the sequence according to the manner above.
Keywords
$\mathbb{Z}_p$-sequences, polynomials, free abelian group