modular roots of unity
The RootsOfUnity(k, n) command computes all the kth roots of unity modulo n.
An integer x is said to be a kth root of unity modulo n if xk=1modn.
unity := RootsOfUnity(5, 8965);
map(x -> x^5 mod 8965, unity);
Distribution of the second roots of unity. A point x,y on the plot denotes that y is a second root of unity modulo x.
plots:-pointplot(select(p -> p^2 mod p = 1, [seq(seq([i,j], j=0..(i-1)), i = 1..1000)]), labels=["Modulus", "Second roots of unity"], labeldirections=[horizontal, vertical]);
The NumberTheory[RootsOfUnity] command was introduced in Maple 2016.
For more information on Maple 2016 changes, see Updates in Maple 2016.
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