The squares of triangular numbers 1 and 6 are triangular numbers 1 and 36.
T1^2 = 1 * 1 = 1 = T1
T3^2 = 6 * 6 = 36 = T8
Are there additional triangular numbers whose squares form a triangular number?
The sum of two consecutive squares, less 1, is the square of the product of two consecutive whole numbers:
N = n(n+1)/2 = s^2 = (m(m+1)/2)^2
2n^2+2n = m^2 (m+1)^2
n^2+(n+1)^21 = (m(m+1))^2

Posted by broll
on 20150112 12:51:54 