摘要
本文研究了当Ｄ含有一个６ｌ＋１型素因数时不定方程ｘ３±（２２ｋ－１）３＝Ｄｙ２的非平凡整数解的个数和求法。
Abstract In this paper we tave intended, among others to prove the following: Theorem1. Suppose are primes, p1 ≡7, 13(mod24), pi≡11(mod12), i=2, …, s, and if exist j, 2≤j≤s satisfy then the equation x3 + (22k-1)3= Dy2, k≥3 ① when K = 4l+3, except Da2=3 (24k-6, + 2k-2) -1, x= 3.24k-6+ 22k-2-1,b = 3.24k-6+1, y= ab maybe produce most one solution (S, x, y), tave not nontrivial integer solution. Except solutions (Di, 4xi, 8yi), solution, where (Di, xi, yi) i= l, 2, …, t are all nontrivial integer solutions of the equation x3+ (22(k-1)-1)3= Dy2. ②when D=4l+l, except Da2= 24k-6+ 3, 22k-2-3, x=24k-6+ 22k-2-3. b=24k-6+ 3,y=ab maybe produce most one solution, tave not nontrivial integer solution.
出处
《黑龙江大学自然科学学报》
CAS
1994年第3期43-46,共4页
Journal of Natural Science of Heilongjiang University
