关于不定方程5x(x 1)(x 2)(x 3) = 42y(y 1)(y 2)(y 3)  

On the Diophantine Equation 5x(x 1)(x 2)(x 3) = 42y(y 1)(y 2)(y 3)

作　　者：张艺宝 

机构地区：[1]西南大学数学与统计学院,重庆

出　　处：《应用数学进展》2024年第5期2105-2109,共5页Advances in Applied Mathematics

摘　　要：本文运用同余式、递推序列和Pell方程等初等方法,证明了不定方程5x(x 1)(x 2)(x 3) = 42y(y 1)(y 2)(y 3)仅有唯一正整数解(x, y) = (6, 3),并找出了该方程的所有整数解。This article uses elementary methods such as congruence formula, recursive sequences, and Pell equation to prove that indefinite Diophantine equation 5x(x 1)(x 2)(x 3) = 42x(x 1)(x 2)(x 3) has a unique positive integer (x, y) = (6, 3). Also, All 20 groups of integer solutions of the equation are found.

关 键 词：不定方程 同余式 PELL方程 正整数解 

分 类 号：O15[理学—数学]