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)
“Flower in the crannied wall,
I pluck you out of the crannies,
I hold you here, root and all, in my hand,
Little flowerbut if I could understand
What you are, root and all, and all in all,
I should know what God and man is.”
—Alfred Tennyson (18091892)
“From cradle to grave this problem of running order through chaos, direction through space, discipline through freedom, unity through multiplicity, has always been, and must always be, the task of education, as it is the moral of religion, philosophy, science, art, politics and economy; but a boys will is his life, and he dies when it is broken, as the colt dies in harness, taking a new nature in becoming tame.”
—Henry Brooks Adams (18381918)
“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)
“Like a man traveling in foggy weather, those at some distance before him on the road he sees wrapped up in the fog, as well as those behind him, and also the people in the fields on each side, but near him all appears clear, though in truth he is as much in the fog as any of them.”
—Benjamin Franklin (17061790)