Order (number theory)
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In number theory, the order of an element a (mod n) is the smallest integer k such that 
Note that the order is only defined when gcd(a,n) = 1, i.e. a and n are coprimes.
By Euler's theorem, the order (mod n) must divide φ(n), Euler's phi function. The order of a primitive root modulo n, by definition, is φ(n).
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