Evaluating Octic Residue Symbols
We detail an algorithm for the evaluation of the 8-power residue symbol. Algorithms for computing r-power residue symbols have only been devised for r ∈ {2, 3, 4, 5, 7}. See [8, 2], [7, 2], [6] and [1] for the cases r = 3, 4, 5 and 7, respectively. As noted in [1], as r grows, the technical details become increasingly complicated. An excellent account on the octic reciprocity can be found in [4, Chapter 9]. See also [3].