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 (1817–1862)
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“Hearing, seeing and understanding each other, humanity from one end of the earth to the other now lives simultaneously, omnipresent like a god thanks to its own creative ability. And, thanks to its victory over space and time, it would now be splendidly united for all time, if it were not confused again and again by that fatal delusion which causes humankind to keep on destroying this grandiose unity and to destroy itself with the same resources which gave it power over the elements.”
—Stefan Zweig (18811942)
“God is a being of transcendent and unlimited perfections: his nature therefore is incomprehensible to finite spirits.”
—George Berkeley (1685–1753)
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—Otis Criblecoblis, U.S. screenwriter. W.C. Fields (W.C. Fields)