关于Diophantine方程S_x(n)=S_y(3)

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

设Sm(n)是第m个n角数,给出了当月n-2为平方数时方程Sx(n)=Sy(3)的全部解的通式,并证明了当n-2为非平方数时该方程有无穷多组正整数解.

Let Sm（n） denote the m-th n-gonal number. The whole positive integer solutions of the Diophantine equation Sx（n） =Sy（3） are given when n 〉6 and n-2 is a square, and it is proved that if n-2 is not a square, and the equation has infinitely many positive integer solutions.