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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“Perhaps the whole root of our trouble, the human trouble, is that we will sacrifice all the beauty of our lives, will imprison ourselves in totems, taboos, crosses, blood sacrifices, steeples, mosques, races, armies, flags, nations, in order to deny the fact of death, which is the only fact we have.”
—James Baldwin (1924–1987)
“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)
“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)
“The finite is annihilated in the presence of the infinite, and becomes a pure nothing. So our spirit before God, so our justice before divine justice.”
—Blaise Pascal (1623–1662)
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Most weary seemed the sea, weary the oar,
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—Alfred Tennyson (1809–1892)