Triangular Roots and Tests For Triangular Numbers
By analogy with the square root of x, one can define the (positive) triangular root of x as the number n such that Tn = x:
An integer x is triangular if and only if 8x + 1 is a square. Equivalently, if the positive triangular root n of x is an integer, then x is the nth triangular number.
Read more about this topic: Triangular Number
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