On the exponential Diophantine equation (4m²+1)ˣ + (21m²-1)ʸ = (5m)ᶻ

IF 0.3 Q4 MATHEMATICS

Annales Mathematicae et Informaticae Pub Date : 2020-01-01 DOI:10.33039/ami.2020.01.003

N. Terai

引用次数: 11

Abstract

Let m be a positive integer. Then we show that the exponential Diophantine equation (4m+1)+(21m−1) = (5m) has only the positive integer solution (x, y, z) = (1, 1, 2) under some conditions. The proof is based on elementary methods and Baker’s method.

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指数丢番图方程(4m²+1)μ k + (21m²-1)↓= (5m)ᶻ

设m为正整数。然后证明了指数型丢芬图方程(4m+1)+(21m−1)= (5m)在某些条件下只有正整数解(x, y, z) =(1,1,2)。证明是基于初等方法和贝克方法。

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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