曲阜师范大学学报（自然科学版）2024，Vol.50Issue(4)：39-44,6.DOI:10.3969/j.issn.1001-5337.2024.4.039
关于Pell方程组x2-39y2=1与y2-Dz2=16的公解
On the common solutions of Pell equations x2-39y2=1 and y2-Dz2=16
摘要
Abstract
By using the methods of congruence,recursive sequence and the properties of the solutions to Pell equation,the following results of the system of Pell equations x2-39y2=1 and y2-Dz2=16 were proved:(1)If D=2n(n ∈ Z+),then it has only trivial solution(x,y,z)=(±25,±4,0);(2)If D=2p1…ps(1≤s≤4,p1,…,ps are distinct odd primes),then it has only trivial solution(x,y,z)=(±25,±4,0)with the exception of D=2 X 1 249;otherwise it has nontrivial solutions(x,y,z)=(±62 425,±9 996,±200).关键词
Pell方程/递归序列/同余/奇素数Key words
Pell equation/recursive sequence/congruence/odd prime分类
数理科学引用本文复制引用
闫档档,杨海,沈秦豫..关于Pell方程组x2-39y2=1与y2-Dz2=16的公解[J].曲阜师范大学学报（自然科学版）,2024,50(4):39-44,6.基金项目
国家自然科学基金(11226038,11371012) （11226038,11371012）
陕西省自然科学基金(2021JM443) （2021JM443）
陕西基础科学研究院科研计划项目(23JSY042). （23JSY042）
