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2013•jOURNAL OF southwest University for NationalitiesRequires access

On solution to the diophantine equation x~3-5~3=Dy~2

Liao Ju

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Abstract

Let D be an odd prime. By using quadratic residue, congruent formula and legendre symbol, two sufficient conditions are obtained that the diophantine equation x3-53=Dy2 has no integer solutions with x≠0(mod5).

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What this paper is about

Let D be an odd prime. By using quadratic residue, congruent formula and legendre symbol, two sufficient conditions are obtained that the diophantine equation x3-53=Dy2 has no integer solutions with x≠0(mod5).

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Available abstract

Let D be an odd prime. By using quadratic residue, congruent formula and legendre symbol, two sufficient conditions are obtained that the diophantine equation x3-53=Dy2 has no integer solutions with x≠0(mod5).

Key concepts: Legendre symbol, Diophantine equation, Quadratic residue, Legendre's equation, Mathematics, Diophantine set, Integer (computer science), Quadratic equation

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