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266:{\displaystyle {\begin{aligned}&\alpha ^{n}=1\\&\sum _{j=0}^{n-1}\alpha ^{jk}=0{\text{ for }}1\leq k<n\end{aligned}}}
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is that it is a necessary condition for the theory of the
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meaning that it is not a principal cube root of unity.
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532:, vol. 1, Boston, MA: Birkhäuser, p. 11
500:{\displaystyle 1+3+3^{2}\equiv 13{\pmod {26}}}
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48:introducing citations to additional sources
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510:The significance of a root of unity being
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415:{\displaystyle 3^{3}\equiv 1{\pmod {26}}}
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38:Relevant discussion may be found on the
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311:-th root of unity. In any ring, if
530:Polynomial and Matrix Computations
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323:/2-th root of −1 is a principal
31:relies largely or entirely on a
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560:. You can help Knowledge by
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528:Bini, D.; Pan, V. (1994),
516:discrete Fourier transform
155:satisfying the equations
59:"Principal root of unity"
352:ring of integers modulo
518:to work out correctly.
148:{\displaystyle \alpha }
556:-related article is a
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44:improve this article
327:-th root of unity.
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444:cube root of unity
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365:{\displaystyle 26}
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612:Cyclotomic fields
607:Algebraic numbers
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435:{\displaystyle 3}
343:{\displaystyle 3}
330:A non-example is
304:{\displaystyle n}
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121:-th root of unity
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632:Polynomial stubs
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627:Complex numbers
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42:. Please help
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55:Find sources:
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33:single source
29:This article
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562:expanding it
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617:Polynomials
319:, then any
113:mathematics
622:1 (number)
601:Categories
554:polynomial
522:References
317:power of 2
117:principal
70:newspapers
512:principal
476:≡
422:and thus
391:≡
282:primitive
248:≤
222:α
213:−
195:∑
172:α
143:α
40:talk page
373:; while
280:, every
100:May 2024
350:in the
131:) of a
129:integer
123:(where
84:scholar
276:In an
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552:This
442:is a
315:is a
91:JSTOR
77:books
558:stub
287:-th
254:<
133:ring
115:, a
63:news
487:mod
402:mod
111:In
46:by
603::
491:26
479:13
446:,
406:26
360:26
589:e
582:t
575:v
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484:(
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399:(
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338:3
325:n
321:n
313:n
299:n
285:n
257:n
251:k
245:1
237:0
234:=
229:k
226:j
216:1
210:n
205:0
202:=
199:j
184:1
181:=
176:n
125:n
119:n
102:)
98:(
88:·
81:·
74:·
67:·
50:.
36:.
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