The Diophantine Equation My(y+1)(y+2)(y+3)=nx(x+1)(x+2)(x+3)

Let m,n∈N,(m,n)=1,the author proves that:1.If m is a perfect square,n=4p2k or n=9p2k,p is a prime,k∈N,then the equation of the title has no positive integer solutions；2.If p is a prime,then the equationy(y+1)(y+2)(y+3)=4p2kx2n1-1(x+1)2n2-1(x+2)2n3-1(x+3)2n4-1, andy(y+1)(y+2)(y+3)=9p2kx2n1-1(x+1)2n2-1(x+2)2n3-1(x+3)2b4-1. has no positive integer solutions x,y,ni(i=1,2,…,4).In particular,we have thatCorollary:If m=1,n=9p2k,p is a prime,then the equatin of the title has no positive integer solutions.