摘要
给出了一类不定方程ｘ３±（５ｋ）３＝Ｄｙ２的全部非平凡整数解．其中Ｄ＞０，无平方因子，且不能被３或６ｌ＋１型的素数整除．
To study the Diophanine equation x3±(5k)3=Dy2The equation x3+(5k)3=Dy2 D≥1, d|D, d is not a square and d is not prime of the form 6l+1, k≥2Just has t+i nontrivial integral solutions(i) the i solutions (i=0 or 1 or 2) are produced from x=14(3·52k+2·5k-1),Da2=x+5k,b=14(3·52k+1),y=ɑb and x=14(52k+2·5k-3),Da2=x+5k,b=14(52k+3),y=ɑb;(ii) the t solution are produced from t solutions (,,) of equation x3+(5k-1)3=Dy2(i) If 5|,then (5,5,25) is the solution of equation x3±(5k)3=Dy2(ii) If 5,then (5,5,5) is the solution of equation x3±(5k)3=Dy2.
出处
《东北师大学报（自然科学版）》
CAS
CSCD
1998年第2期16-19,共4页
Journal of Northeast Normal University(Natural Science Edition)
关键词
丢番图方程
非平凡整数解
同余
Diophantine equation
nontrivial integer solution
modulo
