Liao Ju
Abstract
Let D be an odd prime. By using quadratic residue,congruent formula and legendre symbol,two sufficient conditions are obtained when the Diophantine equation x3-53= 2Dy2has no integer solutions with x ≠0( mod 5).
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Let D be an odd prime. By using quadratic residue,congruent formula and legendre symbol,two sufficient conditions are obtained when the Diophantine equation x3-53= 2Dy2has no integer solutions with x ≠0( mod 5).
Key concepts: Legendre symbol, Diophantine equation, Quadratic residue, Legendre's equation, Mathematics, Diophantine set, Integer (computer science), Prime (order theory)