Root of Unity - Root of Unity in Finite Fields

Root of Unity in Finite Fields

If is a finite field and is a positive integer then a th-root of unity in is a solution of the equation in .

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    At the root of all these noble races, the beast of prey, the splendid blond beast prowling greedily in search of spoils and victory, cannot be mistaken.
    Friedrich Nietzsche (1844–1900)

    Flower in the crannied wall,
    I pluck you out of the crannies,
    I hold you here, root and all, in my hand,
    Little flower—but if I could understand
    What you are, root and all, and all in all,
    I should know what God and man is.
    Alfred Tennyson (1809–1892)

    If usually the “present age” is no very long time, still, at our pleasure, or in the service of some such unity of meaning as the history of civilization, or the study of geology, may suggest, we may conceive the present as extending over many centuries, or over a hundred thousand years.
    Josiah Royce (1855–1916)

    Put shortly, these are the two views, then. One, that man is intrinsically good, spoilt by circumstance; and the other that he is intrinsically limited, but disciplined by order and tradition to something fairly decent. To the one party man’s nature is like a well, to the other like a bucket. The view which regards him like a well, a reservoir full of possibilities, I call the romantic; the one which regards him as a very finite and fixed creature, I call the classical.
    Thomas Ernest Hulme (1883–1917)

    The sun was like a great visiting presence that stimulated and took its due from all animal energy. When it flung wide its cloak and stepped down over the edge of the fields at evening, it left behind it a spent and exhausted world.
    Willa Cather (1873–1947)