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

On the diophantine equation y(y+1)(y+2)(y+3)=19^(2k)x(x+1)(x+2)(x+3)

运用不定方程组的特征以及整除的性质等初等方法,证明了不定方程y(y+1)(y+2)(y+3)=192kx(x+1).(x+2)(x+3)无正整数解.

In this paper, using the characteristics of variable equations and the divisible nature of the elementary method, the paper prove the diophantine equation y（y＋1）（y＋2）（y＋3）=19^2k x（x＋1）（x＋2）（x＋3） no positive integer solutions.