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MultiplicativeOrder

MultiplicativeOrder[k, n]
gives the multiplicative order of k modulo n, defined as the smallest integer m such that

.

MultiplicativeOrder[k, n, {r₁, r₂, ...}]
gives the generalized multiplicative order of k modulo n, defined as the smallest integer m such that

for some i.

MORE INFORMATION

Integer mathematical function, suitable for both symbolic and numerical manipulation.

MultiplicativeOrder returns unevaluated if there is no integer m satisfying the necessary conditions.

Basic Examples (1)

The multiplicative order of 7 modulo 108:

Generalizations & Extensions (1)

Applications (5)

Properties & Relations (2)

EulerPhi PowerMod PrimitiveRoot CarmichaelLambda RealDigits

Integer and Number Theoretic Functions

Cryptographic Number Theory

Diophantine Equations

Mathematical Functions

Number Theoretic Functions

Number Theory

Demonstrations with MultiplicativeOrder (Wolfram Demonstrations Project)

NKS|Online (A New Kind of Science)

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