关于不定方程5x(x + 1)(x + 2)(x + 3) = 19y(y + 1)(y + 2)(y + 3)

On the Diophantine Equation5x(x + 1)(x + 2)(x + 3) = 19y(y + 1)(y + 2)(y + 3)

摘要: 本文运用Pell方程、 二次平方剩余、 递归序列等方法，对不定方程5x(x + 1)(x + 2)(x + 3) = 19y(y + 1)(y + 2)(y + 3) 展开研究，证明了该方程共有16组整数解，且不存在正整数解。

Abstract: In this paper, we use Pell equation, quadratic residue, recursive sequence and other methods to study the 5x(x+1)(x+2)(x+3) = 19y(y +1)(y +2)(y +3) Diophantine equation. It is proved that the equation has 16 groups of integer solutions, and there is no positive integer solution.