摘要
设D=3a^2+1,p=4a^2+1是奇素数,其中a是正整数.本文证明了:当a>6·10^(18)时,方程x^2+D^m=p^n恰有2组正整数解(x,m,n)=(a,1,1)和(8a^3+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 a 〉 6 - 10^18, then the equation x62 ＋ Dm = p^n has exactly two positive integer solutions （x,m, n） = （a,1, 1） and （8a^3 ＋ 3a, 1, 3）.
出处
《数学进展》
CSCD
北大核心
2008年第4期483-488,共6页
Advances in Mathematics（China）
基金
the National Natural Science Foundation of China(No.10771186)
the Guangdong Provincial Natural Science Foundation(No.06029035).
