If a is an arbitrary integer relatively prime to n and g is a primitive root of n, then there exists among the numbers 0, 1, 2, ..., ϕ(n) - 1, where ϕ(n) is the totient function, exactly one number μ such that a congruent g^μ (mod n). The number μ is then called the discrete logarithm of a with respect to the base g modulo n and is denoted μ = ind_g a (mod n). The term "discrete logarithm" is most commonly used in cryptography, although the term "generalized multiplicative order" is sometimes used as well. In number theory, the term "index" is generally used instead.
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