order of a number under modular multiplication
positive integer greater than 1
The MultiplicativeOrder function computes the multiplicative order of m modulo n, which is defined as the least positive integer exponent i such that m^i is congruent to 1 modulo n.
Alternatively, the multiplicative order can be defined as the order of the cyclic group generated by m under multiplication modulo n.
The multiplicative order exists if and only if m and n are coprime. In the case that it does not exist, an error message is displayed.
seq(7^i mod 18, i = 1..3);
If the multiplicative order of m is equal to the totient of n, then m is a primitive root modulo n.
PrimitiveRoot(18, greaterthan = 10);
Since 5 and 25 are not coprime, the multiplicative order of 5 modulo 25 is not defined.
Error, (in NumberTheory:-MultiplicativeOrder) the arguments 5 and 25 are not coprime
The NumberTheory[MultiplicativeOrder] command was introduced in Maple 2016.
For more information on Maple 2016 changes, see Updates in Maple 2016.
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