Departmental Bulletin Paper On Some Diophantine Equations (I)

9 ( 1 )  , pp.75 - 82 , 2018-01独立行政法人国立高等専門学校機構 熊本高等専門学校
ISSN:1884-6734
NCID:09-12
Description
In this paper, we consider two equations (p^x-1)/(q-1)=(q^y-1)/(q-1) and a^(x1)-b^(y1)=a^(x2)-b^(y2)=1. Especially, on (p^x-1)/(q-1)=(q^y-1)/(q-1), we study in the case of y=3 and in the case of p=2. And, without using Catalan’s theorem, we prove that a^(x1)-b^(y1)=a^(x2)-b^(y2)=1 has a unique solution.
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