Mathematics · Advanced university
Order of an element in an additive cyclic group · formula reference
The operation is addition modulo n. Element order is the least positive multiple giving zero.
Formula
The operation is addition modulo n. Element order is the least positive multiple giving zero.
ord([a] in Z/nZ) = n/gcd(a,n)
Worked example
In the additive group Z/41Z, what is the order of the residue class [20]? Round the final result to 4 decimal places if needed.
We need the least positive k with 41 dividing 20k. Divide 41 by gcd(20,41) = 1.
41
Prerequisites and checking
Algebra; calculus or linear algebra as appropriate to the topic. Keep units and rounding consistent. State the model conditions before applying the formula.
Further reading and review references
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