A triple (a, b, c); T_{A} + T_{B} = T_{C}

 
 
Let   (A, \; B, \; C)   be a set of three positive integers for which   T_{A} + T_{B} = T_{C}

Here’s the smallest triangular number of the form   A + B + C   where   (A, \; B, \; C)   is a triangular triple:

(A, \; B, \; C) \; = \; (14, \; 18, \; 23)

(14\times 15)/2 \; + \; (18\times 19)/2 \; = \; 276 \; = \; T_{23}

14 \; + \; 18 \; + \; 23 \; = \; 55 \; = \; T_{10}

 

Find the next triples.

Are there infinitely many such triangular numbers   A + B + C   ?

 
 
Is it possible for the three numbers of a triangular triple to each be triangular?
 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

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About benvitalis

math grad - Interest: Number theory
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