摘要
丢番图方程是经典数论中古老而具有挑战性的问题,一直以来都是数论中的热点问题。文章利用同余的性质、Pell方程的整数解、Maple小程序及二次剩余等方法,对丢番图方程x^3-1=1 477y^2的整数解进行了讨论。研究得出这个方程的平凡整数解和非平凡整数解分别为(x,y)=(1,0)和(x,y)=(212 688,2 552 256)。这一结果为大系数丢番图方程的求解提供了有趣的新思路。
Diophantine equation is an ancient and challenging pioblem in classical number theory. It has always been a hot is-sue in number theory. In this paper, the integer solution of a Diophantine equation x3- 1 = 1 477y2 is studied and discussed by using the properties of congruence, the results of integer solutions of Pell equations, small programs of Maple and quadratic residues. The ordinary integer solution and the nontrivial integer solution of the Diophantine equations are （x,y）= （ 1 ,0 ） and（a;,y） = （212 688, 2 552 256） , respectively. This interesting result provides a new ideal for solving the large coefficients Diophantine equations.
作者
党荣
DANG Rong(ASEAN DPU Institute of Finance and Economics, Weinan Normal University, Weinan 714099, Chin)
出处
《渭南师范学院学报》
2018年第8期11-15,21,共6页
Journal of Weinan Normal University
基金
陕西省科技厅自然科学基金项目:Mock theta函数理论及其交叉应用研究(2016JM1004)
陕西省教育厅专项科研计划项目:Ramanujan mock theta函数的算数性质及其应用研究(17JK0266)
