关于不定方程x^3+1=Dy^2

ON THE INDEFINITE EQUATIONS

对不定方程 x3+ 1 =Dy2 ,当 0 <D<1 0 0 ,不含平方因子 ,且被 6 k+1形的素数整除时 ,本文得到仅当 D=7,1 4,35 ,38,5 7,6 5 ,86时有非平凡整数解 ,并证明 D=91时方程无非平凡解 .

In this paper, we have got that the indefinite equations x 3+1=Dy 2 have nontrivial integer solutions only when D=7,14,35,38,57,65,86, and proved that it has not nontrivial integer solutions if D=91, where 0<D<100, squarefree and is divisible by primes of the form 6k+1.