关于Diophantine方程S_x(n)=S_y(3)

On the Diophantine Equation S_x(n)=S_y(3)

设 Sm(n)是第 m个 n角数 ,给出当 n - 2为平方数时方程 Sx(n) =Sy(3)的全部解的通式 ,并证明当 n

Let Sm(n) denote the m th n gonal number.In this paper,the whole positive integer solutions of the Diophantine equation Sx(n)=Sy(3) are given when n>6 and n-2 is a square.We prove that if n-2 isn't a square,then the equation has infinitely many positive integer solutions.