Problem

Source: China Nanjing , 23 Mar 2014

Tags: number theory proposed, number theory, Diophantine equation, China TST



Show that there are no 2-tuples $ (x,y)$ of positive integers satisfying the equation $ (x+1) (x+2)\cdots (x+2014)= (y+1) (y+2)\cdots (y+4028).$