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)
“The bud of the apple is desire, the down-falling gold,
The catbird’s 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 (1879–1955)
“The Puritans, to keep the remembrance of their unity one with another, and of their peaceful compact with the Indians, named their forest settlement CONCORD.”
—Ralph Waldo Emerson (1803–1882)
“Are not all finite beings better pleased with motions relative than absolute?”
—Henry David Thoreau (1817–1862)
“East and west on fields forgotten
Bleach the bones of comrades slain,
Lovely lads and dead and rotten;
None that go return again.”
—A.E. (Alfred Edward)