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.


Prime Divisor Primitive Root Quadratic Residue Prime Integer Integral Coefficient 
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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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