论文标题
皮莱的多项式猜想
Pillai's conjecture for polynomials
论文作者
论文摘要
在本文中，我们研究了Pillai的猜想的多项式版本在指数二磷酸方程\ BEGIN {等式*} p^n -q^m = f。 \ end {equation*}我们证明，对于任何非恒定多项式$ f $，只有许多矢量$（n，m，m，\ mathrm {deg} \ p，\ mathrm {deg} \ q）$带有integers $ n，m \ geq 2 $ and geq 2 $ and nontonoMialoMial polynomial polynomials $ pills $ pills $ pills pills pills pills pills pills pills pills pills pills pills q。此外，我们将举一些例子，即多项式$ p，q $仍然可能存在许多可能性。
In this paper we study the polynomial version of Pillai's conjecture on the exponential Diophantine equation \begin{equation*} p^n - q^m = f. \end{equation*} We prove that for any non-constant polynomial $ f $ there are only finitely many vectors $ (n,m,\mathrm{deg}\ p,\mathrm{deg}\ q) $ with integers $ n,m \geq 2 $ and non-constant polynomials $ p,q $ such that Pillai's equation holds. Moreover, we will give some examples that there can still be infinitely many possibilities for the polynomials $ p,q $.
