A function field variant of Pillai's problem

@article{Fuchs2020AFF,
  title={A function field variant of Pillai's problem},
  author={Clemens Fuchs and Sebastian Heintze},
  journal={arXiv: Number Theory},
  year={2020}
}
3 Citations
Pillai's conjecture for polynomials
In this paper we study the polynomial version of Pillai’s conjecture on the exponential Diophantine equation p − q = f. We prove that for any non-constant polynomial f there are only finitely many
$ S $-unit values of $ G_n + G_m $ in function fields
In this paper we consider a simple linear recurrence sequence Gn defined over a function field in one variable over the field of complex numbers. We prove an upper bound on the indices n and m such
Asymptotics for Pillai's problem with polynomials
Let a1(x)p1(x)+ · · ·+ak(x)pk(x) n as well as b1(x)q1(x)+ · · ·+ bl(x)ql(x) m be two polynomial power sums where the complex polynomials pi(x) and qj(x) are all non-constant. Then in the present

References

SHOWING 1-10 OF 28 REFERENCES
On Some Exponential Equations of S. S. Pillai
  • M. Bennett
  • Mathematics
    Canadian Journal of Mathematics
  • 2001
Abstract In this paper, we establish a number of theorems on the classic Diophantine equation of S. S. Pillai, ${{a}^{x}}-{{b}^{y}}=c$ , where $a,\,b$ and $c$ are given nonzero integers with
Perfect Powers: Pillai's works and their developments
A perfect power is a positive integer of the form $a^x$ where $a\ge 1$ and $x\ge 2$ are rational integers. Subbayya Sivasankaranarayana Pillai wrote several papers on these numbers. In 1936 and again
ON THE GROWTH OF LINEAR RECURRENCES IN FUNCTION FIELDS
TLDR
This paper proves a function field analogue of the well-known result in the number field case that, under some nonrestrictive conditions, the power sum representation of a nondegenerate linear recurrence sequence is large enough for n to be large enough.
Decomposable polynomials in second order linear recurrence sequences
We study elements of second order linear recurrence sequences $$(G_n)_{n= 0}^{\infty }$$(Gn)n=0∞ of polynomials in $${{\mathbb {C}}}[x]$$C[x] which are decomposable, i.e. representable as
On a problem of Pillai with k–generalized Fibonacci numbers and powers of 2
For an integer $$ k \ge 2 $$k≥2, let $$ \{F^{(k)}_{n} \}_{n\ge 0}$${Fn(k)}n≥0 be the k–generalized Fibonacci sequence which starts with $$ 0, \ldots , 0, 1 $$0,…,0,1 (k terms) and each term
The Catalan equation over function fields
Let K be the function field of a projective variety. Fix a, b, c E K*. We show that if max{m, n} is sufficiently large, then the Catalan equation axm + by c has no nonconstant solutions x, y E K. The
On Some Exponential Equations of
In this paper, we establish a number of theorems on the classic Diophantine equation of S. S. Pillai, a x − b y = c ,w herea, b and c are given nonzero integers with a,b ≥ 2. In particular, we obtain
Diophantine equations
The aim of this paper is to prove the possibility of linearization of such equations by means of introduction of new variables. For n = 2 such a procedure is well known, when new variables are
Effective Bounds for the zeros of linear recurrences in function fields
Dans cet article, on utilise la generalisation de l'inegalite de Mason (due a Brownawell et Masser [8]) afin d'exhiber des bornes superieures effectives pour les zeros d'une suite lineaire recurrente
On Pillai's Diophantine equation.
Let A, B, a, b and c be fixed nonzero integers. We prove several results on the number of solutions to Pillai’s Diophantine equation Aa −Bby = c in positive unknown integers x and y.
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