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==Properties of the Carmichael function==
In this section, an [[integer]] <math>n</math> is divisible by a nonzero integer <math>m</math> if there exists an integer <math>k</math> such that <math>n = km</math>. This is written as
:<math>m \mid n.</math>
===Order of elements modulo ''{{mvar | n}}''===
Let {{mvar | a}} and {{mvar | n}} be [[coprime]] and let {{mvar | m}} be the smallest exponent with {{math | ''a<sup>m</sup>'' ≡ 1 (mod ''n'')}}, then it holds that
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