(n+1)^2/2n+1 是整数 n=?证明思路
问题描述：
(n+1)^2/2n+1 是整数 n=?证明思路
答
由(n+1)^2/(2n+1)是整数,4(n+1)^2/(2n+1)也是整数.而4(n+1)^2/(2n+1) = ((2n+1)(2n+3)+1)/(2n+1) = 2n+3+1/(2n+1),所以1/(2n+1)是整数,这说明2n+1 = 1或-1,对应n = 0或-1.代回验证知n = 0或-1时(n+1)^2/(2n+1)是整数...