Diophantine approximation and the equation (a2cxk−1)(b2cyk−1)=(abczk−1)2(a2cxk−1)(b2cyk−1)=(abczk−1)2

Article ID	Journal	Published Year	Pages	File Type
4593605	Journal of Number Theory	2015	8 Pages	PDF

Abstract

We prove that the Diophantine equation (a2cxk−1)(b2cyk−1)=(abczk−1)2(a2cxk−1)(b2cyk−1)=(abczk−1)2 has no solutions in positive integers with x, y , z>1z>1, k≥7k≥7 and a2xk≠b2yka2xk≠b2yk.

Keywords

Diophantine approximation

Related Topics

Physical Sciences and Engineering Mathematics Algebra and Number Theory

Preview

Diophantine approximation and the equation (a2cxk−1)(b2cyk−1)=(abczk−1)2(a2cxk−1)(b2cyk−1)=(abczk−1)2

Authors

Eva G. Goedhart, Helen G. Grundman,