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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“To those who despair of everything reason cannot provide a faith, but only passion, and in this case it must be the same passion that lay at the root of the despair, namely humiliation and hatred.”
—Albert Camus (19131960)
“Today, supremely, it behooves us to remember that a nation shall be saved by the power that sleeps in its own bosom; or by none; shall be renewed in hope, in confidence, in strength by waters welling up from its own sweet, perennial springs. Not from above; not by patronage of its aristocrats. The flower does not bear the root, but the root the flower.”
—Woodrow Wilson (18561924)
“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)
“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 (16231662)
“Forget about the precious sight
of my lovers face
that steals away my heart.
Just seeing the borders
of the fields on the borders
of her village
gives me instant joy.”
—Hla Stavhana (c. 50 A.D.)