Multiplicative Suborder Sord(a, n)

Sord(a, n) = Multiplicative suborder of base a (mod n) or 0.

See: Suborder Function -- From MathWorld

Here are some notes from my program XICalc - Extra Precision Integer Calculator :

The multiplicative suborder function Sord(a, n) is the minimum positive integer e for which a^e == +/−1 mod n, or zero if no e exists. If a or n is less than 2, zero is returned.

e = Sord(a, n) // e = Multiplicative Suborder // multiplicative suborder of base a (mod n) or zero if it does not exist. // From Stephen Wolfram, Algebraic Properties of Cellular Automata (1984). // Sord = Mord or Mord/2, Mord/2 iff a^(Mord/2) mod n = -1 { e = Mord(a, n) if ((e is odd) or e == 0), return e = e/2 g1 = a^e mod n if (g1 != (n-1)) e = 2*e }

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