The Diophantine equation x~3±(3~K)~3=Dy~2

【摘要】 <正> Ljunggren proved that the equations x~3+1=Dy~2, D>2, d|D, 3D, d is not a square (1) and x~3-1=Dy~2, d is not prime of the form 6l+1 (1)′have one positive integral solution at most. Ko Chao and Sun Chi proved that eqs.(1) and(1)′both have no nontrivial integral solution. In this letter, we prove the following theorems.更多还原