皮莱问题的一个变种，涉及s单位和斐波那契数。

IF 0.9 Q2 MATHEMATICS BOLETIN DE LA SOCIEDAD MATEMATICA MEXICANA Pub Date : 2022-01-01 Epub Date: 2022-07-15 DOI:10.1007/s40590-022-00450-7

Volker Ziegler

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引用次数: 1

摘要

我们用F n表示第n个斐波那契数。本文证明了指数丢芬图方程F n - 2 x 3 y = c有一个以上的解(n, x, y)∈n3且n > 1。而且，在c > 0的情况下，我们发现所有的整数c使得丢番图方程至少有三个解在c > 0的情况下，我们发现所有的整数c使得丢番图方程至少有四个解。

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On a variant of Pillai's problem involving S-units and Fibonacci numbers.

Let us denote by $F_{n}$ the n-th Fibonacci number. In this paper we show that there exist at most finitely many integers c such that the exponential Diophantine equation $F_{n} - 2^{x} 3^{y} = c$ has more than one solution $(n, x, y) \in N^{3}$ with $n > 1$ . Moreover, in the case that $c > 0$ we find all integers c such that the Diophantine equation has at least three solutions and in the case that $c < 0$ we find all integers c such that the Diophantine equation has at least four solutions.