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PowerMod
PowerMod[
a
,
b
,
n
] gives  .
For negative b, PowerMod[
a
,
b
,
n
] gives modular inverses.
Integer mathematical function (see Section A.3.10).
For positive b, PowerMod[
a
,
b
,
n
] gives the same answers as Mod[
a
^
b
,
n
] but is much more efficient.
For negative b, PowerMod[
a
,
b
,
n
] gives the integer  such that  . If no such integer exists, PowerMod returns unevaluated.
See the Mathematica book: Section 3.2.4.
See also: Mod, ExtendedGCD.
Related package: Algebra`PolynomialPowerMod`.
Further Examples
PowerMod is much more efficient than the equivalent combination of Power and Mod.
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