On a Conjecture Concerning the Generalized Ramanujan-Nagell Equation
On a Conjecture Concerning the Generalized Ramanujan-Nagell Equation
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关于广义Ramanujan-Nagell方程的一个猜想
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设D= 3a2 +1，p= 4a2 +1为奇素数，其中a为正整数，本文证明了：当a6·10 18时，方程x2 + Dm = pn有两个正整数解（x，m，n）=（a，1，1）和（8a3 +3a，1，3）.
Let D=3a~2+1 and p=4a~2+1 is an odd prime,where a is a positive integer.In this paper we prove that if a6·10~(18),then the equation x~2+D~m=p~n has exactly two positive integer solutions(x,m,n)=(a,1,1)and(8a~3+3a,1,3).