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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“Perhaps the whole root of our trouble, the human trouble, is that we will sacrifice all the beauty of our lives, will imprison ourselves in totems, taboos, crosses, blood sacrifices, steeples, mosques, races, armies, flags, nations, in order to deny the fact of death, which is the only fact we have.”
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“Black creeps from root to root,
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“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.”
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“Are not all finite beings better pleased with motions relative than absolute?”
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“The hunt is up, the morn is bright and grey,
The fields are fragrant and the woods are green.”
—William Shakespeare (1564–1616)