2010Journal of Foshan UniversityRequires access

On the diophantine equation of x~3-1=Dy~2

Tan Kai-fa

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Abstract

It is proved that the diophantine equation,x3-1=py2,has only one solution(x,y)=(1,0) on condition that t were an integer and p=12t2+1 were a prime.

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What this paper is about

It is proved that the diophantine equation,x3-1=py2,has only one solution(x,y)=(1,0) on condition that t were an integer and p=12t2+1 were a prime.

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Available abstract

It is proved that the diophantine equation,x3-1=py2,has only one solution(x,y)=(1,0) on condition that t were an integer and p=12t2+1 were a prime.

Key concepts: Diophantine equation, Legendre's equation, Mathematics, Pure mathematics

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