Zhiping Li
Abstract
Let p be an odd prime.This paper studies the positive integer solutions situation of the Diophantine equation x3+1=3py2.Using elementary theory of numbers methods,a sufficient condition is obtained that Diophantine equation without integer solution,i.e.is a prime,is a nonnegative integers,then the equation has no positive integer solution.
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Let p be an odd prime.This paper studies the positive integer solutions situation of the Diophantine equation x3+1=3py2.Using elementary theory of numbers methods,a sufficient condition is obtained that Diophantine equation without integer solution,i.e.is a prime,is a nonnegative integers,then the equation has no positive integer solution.
Key concepts: Diophantine equation, Integer (computer science), Mathematics, Diophantine set, Legendre's equation, Prime (order theory), Prime factor, Radical of an integer