Bases for integer-valued polynomials in a Galois field
A characterization of rational elements by Lüroth-type series expansions in the p-adic number field and in the field of Laurent series over a finite field
Quasi-permutation polynomials
A quasi-permutation polynomial is a polynomial which is a bijection from one subset of a finite field onto another with the same number of elements. This is a natural generalization of the familiar permutation polynomials. Basic properties of quasi-permutation polynomials are derived. General criteria for a quasi-permutation polynomial extending the well-known Hermite's criterion for permutation polynomials as well as a number of other criteria depending on the permuted domain and range are established....
Independence measures of arithmetic functions II
A characterization of rational numbers by p-adic Sylvester series expansions
The positivity problem for fourth order linear recurrence sequences is decidable
The problem whether each element of a sequence satisfying a fourth order linear recurrence with integer coefficients is nonnegative, referred to as the Positivity Problem for fourth order linear recurrence sequence, is shown to be decidable.
Some logarithmic functional equations
The functional equation is solved for general solution. The result is then applied to show that the three functional equations , and are equivalent. Finally, twice differentiable solution functions of the functional equation are determined.
Properties of rational arithmetic functions.
Combinatorial aspects of the generalized Euler's totient.
Completely multiplicative functions arising from simple operations.
Multiply integer-valued polynomials in a Galois field.
An addendum to the paper: “Arithmetic functions over rings with zero divisors” by Ruangsinsap, Laohakosol and P. Udomkavanich.
Rational recursive equations characterizing cotangent-tangent and hyperbolic cotangent-tangent functions.
Cauchy's functional equation in restricted complex domains.
Ramanujan sums via generalized Möbius functions and applications.
Arithmetic functions over rings with zero divisors.
Characterizing completely multiplicative functions by generalized Möbius functions.
Values taken by linear combinations of cosine functions.
Power function solutions of iterative functional differential equations.
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