The multiplicative suborder of a number a (mod n) is the least exponent e>0 such that a^e congruent ± 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 ]

multiplicative order