| 11. | Washington wrote a standard work on cyclotomic fields.
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| 12. | Many restrictions are known about the values that cyclotomic polynomials can assume at integer values.
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| 13. | The cyclotomic polynomials are monic polynomials with integer coefficients that are palindromics of even degree.
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| 14. | Kummer used these as a substitute for the failure of unique factorization in cyclotomic fields.
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| 15. | The first two class field theories were very explicit cyclotomic and complex multiplication class field theories.
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| 16. | As with cyclotomic fields more generally, the field of Gaussian rationals is neither countably infinite.
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| 17. | Also, cyclotomic polynomials are palindromic.
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| 18. | Here and are ordinary integers, whereas the factors are algebraic integers in the cyclotomic field.
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| 19. | A theorem of Schur says that there are cyclotomic polynomials with coefficients arbitrarily large in absolute value.
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| 20. | There are two slightly different definitions of the term "'cyclotomic extension . "'
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