The Diophantine equation f(x) = g(y)

172 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

ON RITT'S POLYNOMIAL DECOMPOSITION THEOREMS (2008, background): “Since Ritt’s results have been generalized to the setting of Laurent polynomials [7, 30, 40], this gives information about decompositions of f 〈i〉 and g〈j〉, which leads to the application of Theorem 1.”
Prime and composite Laurent polynomials (2007, methodology): “The final result is the following statement which supplements (over the field C) Theorem 6.1 of the paper of Bilu and Tichy [3].”
Linear relations between polynomial orbits (2008, background): “In this section we analyze f, g ∈ C[X] which are commensurable, in the sense that for every m ∈ N there exist n ∈ N and h1, h2 ∈ C[X] such that f 〈n〉 = g〈m〉 ◦ h1 and g〈n〉 = f 〈m〉 ◦ h2.”
Generalized balancing numbers (2009, methodology): “The next lemma is based on a recent deep theorem of Bilu and Tichy [4], as well as on the undecomposability of the Bernoulli polynomials proved by Bilu et al.”
Intersections of polynomial orbits, and a dynamical Mordell–Lang conjecture (2007, methodology): “Based on this principle, dozens of recent papers have applied the Bilu-Tichy criterion when F and G come from basically any class of polynomials one can think of: Bernoulli polynomials, falling factorials, power-sum polynomials, Taylor polynomials for ex, Jacobi polynomials, Laguerre polynomials, He”