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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“The root of the problem is not so much that our people have lost confidence in government, but that government has demonstrated time and again its lack of confidence in the people.”
—Jimmy Carter (James Earl Carter, Jr.)
“In dark places and dungeons the preacher’s words might perhaps strike root and grow, but not in broad daylight in any part of the world that I know.”
—Henry David Thoreau (1817–1862)
“I therefore, the prisoner in the Lord, beg you to lead a life worthy of the calling to which you have been called, with all humility and gentleness, with patience, bearing with one another in love, making every effort to maintain the unity of the Spirit in the bond of peace.”
—Bible: New Testament, Ephesians 4:1-3.
“We know then the existence and nature of the finite, because we also are finite and have extension. We know the existence of the infinite and are ignorant of its nature, because it has extension like us, but not limits like us. But we know neither the existence nor the nature of God, because he has neither extension nor limits.”
—Blaise Pascal (1623–1662)
“But famished field and blackened tree
Bear flowers in Eden never known.
Blossoms of grief and charity
Bloom in these darkened fields alone.”
—Edwin Muir (1887–1959)