Positive Integer. (?) = (?) Solution

It has nearly one thousand years'histories of binomial coefficients. Binomial coefficients have extremely close relation with Bernoulli numbers, Catalan num-bers, Fibonacci numbers and many other combinatorial problems, (3x) and (2y) are called tetrahedral number and triangular number respectively, which people cared as early as Pythagoras [4]. It's interesting to consider which numbers belong to two kinds of figurate numbers.The problem that triangle equals tetrahedron, i.e, (3x)= (2y) was solved by E. T. Avanesov [2] in 1967. The only nontrivial positive integral solutions are (x,y)= (16,10),(56,22),(120,36).For 2≤k≤n-1, define an analogue of the binomial coefficient called double factorial of binomial coefficient, which satisfies (kn)!!= ((n-k)n)!! and when n= k, (kn)!!=1. In 2009, Xiaå'ŒCai [3] considered in which case (kn)!! is a power of a rational number.In this paper, we get all the nontrivial positive integral solutions of a new diophantine equation (3x)!!=(2y)!!, by using the methods of factorization in prime ideals and Thue equation.