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The numbers 1 and 36 are both square and triangular. Find the smallest number greater than 36 that is square and triangular.

 Jun 13, 2019
 #1
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+2

  The square  triangular  numbers  , after 1, are

 

So   [ C(9, 7)]  =    9! / [ 2! * 7! ] =  (9 * 8) / 2  =   9* 4  = 36   

 

The next number occurs at   C(50,48)  =  (50!) /[ 48! * 2! ]  =  [50* 49] / 2 = 25*49  = 1225

 

 

 

 

cool cool cool

 Jun 13, 2019
edited by CPhill  Jun 13, 2019
 #2
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+1

Here are all the triangular numbers that are squares up to 1,000,000:
1                   = 1
6                   = 36
35                 = 1,225
204               = 41,616
1189             = 1,413,721
6930             = 48,024,900
40391           = 1,631,432,881
235416         = 55,420,693,056

 Jun 13, 2019

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