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 .

Read more about this topic:  Root Of Unity

Famous quotes containing the words root of, root, unity, finite and/or fields:

    The root of the problem is not so much that our people have lost confidence in government, but that government has demonstrated time and again its lack of confidence in the people.
    Jimmy Carter (James Earl Carter, Jr.)

    I will go root away
    The noisome weeds which without profit suck
    The soil’s fertility from wholesome flowers.
    William Shakespeare (1564–1616)

    From cradle to grave this problem of running order through chaos, direction through space, discipline through freedom, unity through multiplicity, has always been, and must always be, the task of education, as it is the moral of religion, philosophy, science, art, politics and economy; but a boy’s will is his life, and he dies when it is broken, as the colt dies in harness, taking a new nature in becoming tame.
    Henry Brooks Adams (1838–1918)

    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)

    I respect not his labors, his farm where everything has its price, who would carry the landscape, who would carry his God, to market, if he could get anything for him; who goes to market for his god as it is; on whose farm nothing grows free, whose fields bear no crops, whose meadows no flowers, whose trees no fruit, but dollars; who loves not the beauty of his fruits, whose fruits are not ripe for him till they are turned to dollars. Give me the poverty that enjoys true wealth.
    Henry David Thoreau (1817–1862)