In this paper, we study the equation of the title with D general. The equation has nontrivial integer solutions, only when D=7, 26, 31, 38 or 61, for 0
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倪谷炎.关于不定方程x3=Dy2+1[J].国防科技大学学报,1999,21(5):109-111. Ni Guyan. On The Diophantine Equation x3=Dy2+1[J]. Journal of National University of Defense Technology,1999,21(5):109-111.