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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“There is a certain class of unbelievers who sometimes ask me such questions as, if I think that I can live on vegetable food alone; and to strike at the root of the matter at once,for the root is faith,I am accustomed to answer such, that I can live on board nails. If they cannot understand that, they cannot understand much that I have to say.”
—Henry David Thoreau (18171862)
“The bud of the apple is desire, the down-falling gold,
The catbirds gobble in the morning half-awake
These are real only if I make them so. Whistle
For me, grow green for me and, as you whistle and grow green,
Intangible arrows quiver and stick in the skin
And I taste at the root of the tongue the unreal of what is real.”
—Wallace Stevens (18791955)
“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 (18551916)
“For it is only the finite that has wrought and suffered; the infinite lies stretched in smiling repose.”
—Ralph Waldo Emerson (18031882)
“The foolish fears of what might happen.
I cast them all away
Among the clover-scented grass,
Among the new-mown hay,
Among the husking of the corn,
Where drowsy poppies nod
Where ill thoughts die and good are born
Out in the fields with God.”
—Elizabeth Barrett Browning (18061861)