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MultiplicativeOrder

MultiplicativeOrder
gives the multiplicative order of k modulo n, defined as the smallest integer such that .
MultiplicativeOrder
gives the generalized multiplicative order of k modulo n, defined as the smallest integer such that for some .
  • Integer mathematical function, suitable for both symbolic and numerical manipulation.
  • MultiplicativeOrder returns unevaluated if there is no integer satisfying the necessary conditions.
The multiplicative order of 7 modulo 108:
The multiplicative order of 7 modulo 108:
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Click for copyable input
Out[1]=
Evaluate for large arguments:
MultiplicativeOrder works for negative first arguments:
TraditionalForm formatting:
Generalized multiplicative order:
Find all primitive roots modulo 43:
Find a solution to Mod[5^k, 7]=2:
The function gives the digit period for any rational number r in base b:
This shows that the decimal representation of in base repeats every digits.
The digits of in base repeat with period :
The repetition period in Rule 90 for odd n divides :
EulerPhi is a multiple of the multiplicative order:
The multiplicative order of a primitive root modulo n is EulerPhi[n]:
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