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T times T creates another T?? (Posted on 2015-01-11) Difficulty: 4 of 5
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?

See The Solution Submitted by Ady TZIDON    
Rating: 4.0000 (1 votes)

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Some Thoughts An equivalent problem | Comment 5 of 8 |

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)^2-1 = (m(m+1))^2 



  Posted by broll on 2015-01-12 12:51:54
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