Fill in each blank with an answer as easy as possible.(a)M is a triangular number if and only if___________ is an odd square number.(b)N is an odd square number if and only if____________is a triangular number.triangular number:n(n+1)/2,square number:n^2.
问题描述：
Fill in each blank with an answer as easy as possible.
(a)M is a triangular number if and only if___________ is an odd square number.
(b)N is an odd square number if and only if____________is a triangular number.
triangular number:n(n+1)/2,square number:n^2.
答
8a+1
(b-1)/8
答
(a)
M = n(n+1)/2
等价于：8M+1 = 4 n^2 + 4 n + 1 = (2n+1)^2
所以,第1个空应该填：8M+1
(b)
N = (2n+1)^2
等价于：(N-1) / 8 = n(n+1)/2
所以,第2个空应该填：(N-1)/8