关于不定方程 x3±8＝19 y2

安莹,罗明

doi:10.13718/j.cnki.xsxb.2014.12.003

西南师范大学学报(自然科学版)

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关于不定方程 x3±8＝19 y2

安莹,罗明. 关于不定方程 x3±8＝19 y2[J]. 西南师范大学学报(自然科学版), 2014, 39(12). doi: 10.13718/j.cnki.xsxb.2014.12.003

引用本文:

安莹,罗明. 关于不定方程 x3±8＝19 y2[J]. 西南师范大学学报(自然科学版), 2014, 39(12). doi: 10.13718/j.cnki.xsxb.2014.12.003

AN Ying,LUO Ming. On the Diophantine Equation x3 ± 8=19 y2[J]. Journal of Southwest China Normal University(Natural Science Edition), 2014, 39(12). doi: 10.13718/j.cnki.xsxb.2014.12.003

Citation:

AN Ying,LUO Ming. On the Diophantine Equation x3 ± 8=19 y2[J]. Journal of Southwest China Normal University(Natural Science Edition), 2014, 39(12). doi: 10.13718/j.cnki.xsxb.2014.12.003

关于不定方程 x3±8＝19 y2

安莹,罗明

西南大学数学与统计学院,重庆400715; 和田师范专科学校数学系,新疆和田848000 ; 西南大学数学与统计学院,重庆,400715

On the Diophantine Equation x3 ± 8=19 y2

AN Ying,LUO Ming

摘要: With the elementary method of Pell equation ,recurrent sequence ,congruent formula ,quadratic residue ,and Jacobi symbol ,it has proved that the Diophantine equation x3 +8=19y2 has only the integer solutions of (-2 ,0) ,(62 ,± 112) ,and the Diophantine equation x3 -8=19y2 has only the integer solu‐tions of (x ,y)= (2 ,0) ,(3 , ± 1) ,(14 , ± 12) .In the process of proving the conclusion ,the authors cor‐rected the conclusion that the Diophantine equation x3 -1=38 y2 has only the integer solutions of (x ,y)=(1 ,0) ,and then prove all integer solutions of x3 -1=38y2 are (x ,y)= (1 ,0) ,(7 ± 3) .
- Diophantineequation,integersolution,recurrentsequence
Abstract: 不定方程；整数解；递归序列

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关于不定方程 x3±8＝19 y2

安莹,罗明

西南大学数学与统计学院,重庆400715; 和田师范专科学校数学系,新疆和田848000 ; 西南大学数学与统计学院,重庆,400715

关键词:

Diophantineequation,integersolution,recurrentsequence

摘要: With the elementary method of Pell equation ,recurrent sequence ,congruent formula ,quadratic residue ,and Jacobi symbol ,it has proved that the Diophantine equation x3 +8=19y2 has only the integer solutions of (-2 ,0) ,(62 ,± 112) ,and the Diophantine equation x3 -8=19y2 has only the integer solu‐tions of (x ,y)= (2 ,0) ,(3 , ± 1) ,(14 , ± 12) .In the process of proving the conclusion ,the authors cor‐rected the conclusion that the Diophantine equation x3 -1=38 y2 has only the integer solutions of (x ,y)=(1 ,0) ,and then prove all integer solutions of x3 -1=38y2 are (x ,y)= (1 ,0) ,(7 ± 3) .