关于方程S_x(n)=S_y(3)  

On the Equations S_x(n) = S_y(3)

作　　者：李中[1] 

机构地区：[1]茂名学院数学系,广东茂名525000

出　　处：《中山大学学报论丛》2001年第3期49-51,共3页Supplement to the Journal of Sun Yatsen University

摘　　要：对于正整数ｍ，ｎ（ｎ≥３），设Ｓｍ（ｎ）是第ｍ个ｎ角数．证明：当ｎ＞６且ｎ－２是平方数时，方程Ｓｘ（ｎ）＝ Ｓｙ（３）无正整数解（ｘ，ｙ）；当ｎ＞６，２　ｎ且ｎ－２为非平方数时，该方程有无穷多组正整数解（ｘ，ｙ）．For any positive integers m, n with n≥3, Let Sm(n) denote the m - th n - gonal number. It is shown that ① if n>6and n-2 is a perfect square, then the equation Sx(n) = Sy(3) has no positive integer solution (x, y); ② if n >6, 2 n and n -2 is not a perfect square, then the equation has infinitely many positive integer solutions (x, y).

关 键 词：多角数 DIOPHANTUS方程 可解性 

分 类 号：O156[理学—数学]