关于Ramanujan-Nagell型方程x^2+2~n=B

On Ramanujan-Nagell Type Equation x^2+2~n=B

证明了对任意正整数B,Ramanujan-Nagell型方程x2+2n=B的非负整数解(x,n)的组数不超过3,从而解决了Ulas关于Ramanujan-Nagell型方程x^2+k^n=B在k=2时的解数猜测.

In this paper,it was proved that for any positive integer B,the number of solutions in nonnegative integer（x,n）of the Ramanujan-Nagell type equation x^2＋2^n=Bis at most 3,which solved the case k=2 of a conjecture of Ulas to the number of solutions of Ramanujan-Nagell type equation x^2＋k^n=B.