关于不定方程5x(x+1)(x+2)(x+3)=9y(y+1)(y+2)(y+3)  

On the Diophantine Equation5x(x+1)(x+2)(x+3)=9y(y+1)(y+2)(y+3)

作　　者：谢耀兵 XIE Yao-bing(School of Mathematics and Statistics,Southwest University,Chongqing 400715,China)

机构地区：[1]西南大学数学与统计学院,重庆400715

出　　处：《数学的实践与认识》2022年第5期246-249,共4页Mathematics in Practice and Theory

摘　　要：运用pell方程、递归序列、二次平方剩余的方法,并使用数学软件Mathematica的计算,求出了丢番图方程5x(x+1)(x+2)(x+3)=9y(y+1)(y+2)(y+3)的所有20组整数解,其中只有一组正整数解为(x,y)=(6,5).In this paper,with the primary methods of Pell equation,recurrence sequences,quadratic remainders and the software Matiematic,the author show that the diophantine equation5 x(x+1)(x+2)(x+3)=9 x(x+1)(x+2)(x+3)has a unique positive integer(x,y)=(6,5).Also,All 20 groups of integer solutions of the equation are found.

关 键 词：不定方程 整数解 平方剩余 递归序列 

分 类 号：O156[理学—数学]