Triangular Number - Triangular Roots and Tests For Triangular Numbers

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

Famous quotes containing the words roots, tests and/or numbers:

    Now fades the lasts long streak of snow,
    Now burgeons every maze of quick
    About the flowering squares, and thick
    By ashen roots the violets blow.
    Alfred Tennyson (1809–1892)

    The secret of a leader lies in the tests he has faced over the whole course of his life and the habit of action he develops in meeting those tests.
    Gail Sheehy (b. 1937)

    The land cannot be cleansed of the blood that is shed therein, but by the blood of him that shed it.
    —Bible: Hebrew Numbers 35:33.