PowerMod[a, b, m]
gives .

PowerMod[a, -1, m]
finds the modular inverse of a modulo m.

PowerMod[a, 1/r, m]
finds a modular r^(th) root of a.


  • Integer mathematical function, suitable for both symbolic and numerical manipulation.
  • For positive b, PowerMod[a, b, m] gives the same result as Mod[a^b, m] but is much more efficient.
  • PowerMod[a, b, m] allows negative and rational values of b. It returns unevaluated if the corresponding modular inverse or root does not exist.
  • PowerMod automatically threads over lists.
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