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.)
“A radical generally meant a man who thought he could somehow pull up the root without affecting the flower. A conservative generally meant a man who wanted to conserve everything except his own reason for conserving anything.”
—Gilbert Keith Chesterton (18741936)
“Certainly for us of the modern world, with its conflicting claims, its entangled interests, distracted by so many sorrows, so many preoccupations, so bewildering an experience, the problem of unity with ourselves in blitheness and repose, is far harder than it was for the Greek within the simple terms of antique life. Yet, not less than ever, the intellect demands completeness, centrality.”
—Walter Pater (18391894)
“All finite things reveal infinitude:”
—Theodore Roethke (19081963)
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—Henry David Thoreau (18171862)