Diophantus方程sun from i=0 to n(x+i)~2=y^2的正整数解(Ⅰ)

Positive Integral Solutions of The Diophantus Equation sun from i=0 to n(x+i)~2=y^2(n≤50)

探讨Diophantus方程Σni=0 (x +i) 2 =y2 在n≤ 5 0下的正整数解问题 ,得到了以下结果 :Diophantus方程 Σni=0 (x+i) 2 =y2 在n≤ 5 0下有正整数解的充要条件为n∈ {1 ,1 0 ,2 2 ,2 3 ,2 5 ,3 2 ,46,48,49}.

In this paper,we obtain that the Diophantus equation sun from i=0 to n(x+i)~2=y^2(n≤50)exists positive integral if and only if n∈{1,10,22,23,25,32,46,48,49}.