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Abstract

Now we will consider equations of the form x m = a, in a field K (or occasionally in a ring); the case a=1 has been discussed in § X. As the case a=0 is trivial, we assume a≠0. If then, in the field K, x is a solution of xm=a, an element x’ of K is also a solution if and only if (x’/x) m =1. Therefore, if xm=a has a solution in K, it has as many solutions as K contains mth roots of unity, i.e. roots of X m -1.

Keywords

Prime Divisor Primitive Root Quadratic Residue Prime Integer Integral Coefficient 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York Inc. 1979

Authors and Affiliations

  • André Weil
    • 1
  1. 1.Institute for Advanced StudyPrincetonUSA

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