Thursday 29 December 2016

How to find Triangular Numbers

I read that Gauss's Eureka Theorem says that any positive integer can be represented by at most 3 triangular numbers. So say I have some positive integer X, how do I find which 3 triangular numbers added together make that Number X?



edit: if there isn't a way to do this without just guessing and combining all combinations of 3 triangular numbers less than X, then is there a program that can do it for me?



edit 2: It looks like for some integers that there is more than 1 way to describe them using 3 triangular numbers. The way to calculate the possible number of ways is using this formula: enter image description here




http://www.3quarksdaily.com/3quarksdaily/2015/03/last-month-at-3qd-we-discovered-that-while-it-was-invented-to-solve-problems-in-counting-and-probability-pascals-triangle-c.html



I still don't know if there is a formula to find which triangular numbers though :(

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