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2009•Journal of Sichuan University of Science & EngineeringRequires access

On the Diophantine Equations x+1=6py~2,x~2-x+1=3z~2

Wang Chun-yan

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Abstract

Let p be a prime,this paper uses congruence and some result of high degree Diophantine equation to prove that the Diophantine equation x+1=6py2,x2-x+1=3z2does not have positive integer solution.

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What this paper is about

Let p be a prime,this paper uses congruence and some result of high degree Diophantine equation to prove that the Diophantine equation x+1=6py2,x2-x+1=3z2does not have positive integer solution.

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Available abstract

Let p be a prime,this paper uses congruence and some result of high degree Diophantine equation to prove that the Diophantine equation x+1=6py2,x2-x+1=3z2does not have positive integer solution.

Key concepts: Diophantine equation, Diophantine set, Mathematics, Physics, Pure mathematics

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