在Pell方程的y坐标上它是以2个代表数字为基数的

Pub Date : 2020-06-12 DOI:10.3336/gm.55.1.01

Bernadette Faye-Fall, F. Luca, Unam Morelia Mexico Centro de Ciencias Matemáticas

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引用次数: 5

摘要

．本文证明了对于非平方整数d > 1，如果(X k, Y k)是Pell方程x2−dY 2 = 1的第k个解，则方程Y k = 2n−1最多有两个正整数解(k,n)。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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On Y-coordinates of Pell equations which are base 2 rep-digits

. In this paper, we show that if ( X k ,Y k ) is the k th solution of the Pell equation X 2 − dY 2 = 1 for some non–square integer d > 1, then the equation Y k = 2 n − 1 has at most two positive integer solutions ( k,n ).

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