Suborder Function

The multiplicative suborder of a number a (mod n) is the least exponent e>0 such that a^e=+/-1 (mod n), or zero if no such e exists. An e always exists if GCD(a,n)=1 and n>1.

This function is denoted sord_n(a) and can be implemented in the Wolfram Language as:

 Suborder[a_,n_] := If[n>1&& GCD[a,n] == 1,
 Min[MultiplicativeOrder[a, n, {-1, 1}]],
 0
 ]

The following table summarizes sord_n(a) for small values of a and n.

See also

This entry contributed by Tony Noe

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References

Referenced on Wolfram|Alpha

Cite this as:

Noe, Tony. "Suborder Function." From MathWorld--A Wolfram Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/SuborderFunction.html

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