摘要
先后运用了pell方程、勒让德符号,同余关系,递归序列、二次平方剩余,分类讨论的有关方法,并通过使用数学软件Mathematica进行计算,证明了以下结论:不定方程x(x+1)(x+2)(x+3)=27y(y+1)(y+2)(y+3)没有正整数解,并找出了该方程的全部16组整数解.
In this paper,Pell equation,Legendre symbol,congruence relation,recursive sequence,quadratic squareresidue,and related methods of classified discussion have been usedsuccessively,and by using mathematical software Mathematica to calculate,thefollowing conclusions have been proved:the indefinite equation x(x+1)(x+2)(x+3)=27y(y+1)(y+2)(y+3) has no positive integer solution,and all 16 groups ofinteger solutions of the equation have been found.
作者
张芊
ZHANG Qian(School of Mathematics and Statistics,Southwest University,Chongqing 400715,China)
出处
《数学的实践与认识》
2023年第3期284-290,共7页
Mathematics in Practice and Theory
关键词
不定方程
勒让德符号
整数解
平方剩余
分类讨论
递归序列
diophantine equation
legendre symbol
positive integersolution
quadratic remainder
categorical discussion
recurrence sequence