p-adic Dedekind sums.
Padovan and Perrin numbers as products of two generalized Lucas numbers
Let and be the -th Padovan and Perrin numbers respectively. Let be non-zero integers with and , let be the generalized Lucas sequence given by , with and In this paper, we give effective bounds for the solutions of the following Diophantine equations where , and are non-negative integers. Then, we explicitly solve the above Diophantine equations for the Fibonacci, Pell and balancing sequences.
Padua and Pisa are exponentially far apart.
We answer the question posed by Ian Stewart which Padovan numbers are at the same time Fibonacci numbers. We give a result on the difference between Padovan and Fibonacci numbers, and on the growth of Padovan numbers with negative indices.
Parity theorems for statistics on domino arrangements.
Partial fraction decompositions and Kummer congruences for the normalized coefficients of the Laurent expansion of elliptic functions parametrizing a nonsingular cubic curve in Hessian normal form.
Pell and Pell-Lucas numbers of the form
In this paper, we find all Pell and Pell-Lucas numbers written in the form , in nonnegative integers , , , with .
Pentagonal numbers in the Lucas sequence.
Perfect squares in the sequence .
Periodic analogues of the Euler-Maclaurin and Poisson summation formulas with applications to number theory
Periodic harmonic functions on lattices and points count in positive characteristic
This survey deals with pluri-periodic harmonic functions on lattices with values in a field of positive characteristic. We mention, as a motivation, the game “Lights Out” following the work of Sutner [20], Goldwasser- Klostermeyer-Ware [5], Barua-Ramakrishnan-Sarkar [2, 19], Hunzikel-Machiavello-Park [12] e.a.; see also [22, 23] for a more detailed account. Our approach uses harmonic analysis and algebraic geometry over a field of positive characteristic.
Periodic sequences of pseudoprimes connected with Carmichael numbers and the least period of the function
Periodicity and parity theorems for a statistic on -mino arrangements.
Planar Realizations of Nonlinear Davenport-Schinzel Sequences by Segments.
Polynômes eulériens modulo
Polynomials generated by the Fibonacci sequence.
Power values of certain quadratic polynomials
In this article we compute the th power values of the quadratic polynomials with negative squarefree discriminant such that is coprime to the class number of the splitting field of over . The theory of unique factorisation and that of primitive divisors of integer sequences is used to deduce a bound on the values of which is small enough to allow the remaining cases to be easily checked. The results are used to determine all perfect power terms of certain polynomially generated integer...
Preface
Primality tests using algebraic groups.
Prime divisors of Lucas sequences
Prime divisors of some shifted products.