Study On The Diophantine Equation X(x+1)(x+2)(x+3)=Dy(y+1)(y+2)(y+3)

The solution of this Diophantine Equation:x(x+1)(x+2)(x+3)=Dy(y+1)(y+2)(y+3),is unsolved in number theory,where D is a fixed positive integer.Based on the previous research of the diophantine equation,we solved this situation where D=22 and D=29 by utilizing the fundamental solution properties of Pell equation,congruence,Legendre symbol and recursive sequence.Eventually,we have resolved the all circumstances that D is not more than 30 that is 0<D ?30 and D ? Z.Conclusion:1.The diophantine equation x(x+1)(x+2)(x+3)=22y(y+1)(y+2)(y+3)has only two positive integer solutions:(x,y)=(8,3)or(32,14).2.The diophantine equation x(x+1)(x+2)(x+3)=29y(y+1)(y+2)(y+3)has no positive integer solution.