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)
“Flower in the crannied wall,
I pluck you out of the crannies,
I hold you here, root and all, in my hand,
Little flower—but if I could understand
What you are, root and all, and all in all,
I should know what God and man is.”
—Alfred Tennyson (1809–1892)
“The gifts he gave were that some would be apostles, some prophets, some evangelists, some pastors and teachers, to equip the saints for the work of ministry, for building up the body of Christ, until all of us come to the unity of the faith and of the knowledge of the Son of God, to maturity, to the measure of the full stature of Christ.”
—Bible: New Testament, Ephesians 4:11.
“For it is only the finite that has wrought and suffered; the infinite lies stretched in smiling repose.”
—Ralph Waldo Emerson (1803–1882)
“I never vote for anyone. I always vote against.”
—W.C. Fields (1879–1946)