Wikipedia:Reference desk/Archives/Mathematics/2017 September 13

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September 13

Fractional exponent in discrete modular exponentiation

Can fractional exponents exist in discrete exponential function, both ordinary and modular exponentiation, especially with examples like modular square root, modular cube root etc, where the order of the root n is an 1/n fractional discrete exponent?(Thanks).--82.137.9.243 (talk) 13:36, 13 September 2017 (UTC)

I think modular exponentiation refers to a method of finding exponents over a given modulus rather than a different type of exponentiation. So while n^1/2 may exist under a given modulus, that doesn't mean modular exponentiation is useful for finding its value. Turns out that most methods of computing n^1/2 do involve finding integer exponents (see Quadratic residue#Complexity of finding square roots, and presumably you would use modular exponentiation to find these, but it's not a simple generalization. --RDBury (talk) 18:51, 14 September 2017 (UTC)