both with real analysis and by using residue calculus

*edit: i did a mistake so i dont know if its possible to do this using residues, but that does not mean it must be impossible*

sure！ it's right

\sum_{k=1}^n \zeta_k^m =0

it does not hold for all m and n

]]>Welcome to the forum.

You forgot to enclose your latex between {math}{/math} with [ replacing { and ] replacing } so it looks like this:

Anyway, how does this prove # 14

]]>\sum_{k=1}^n \zeta_k^m =0

]]>Will you please post your solution to #7. I have been using summation by parts, abels transformation, exponential substitution to get a geometric sum and all the trig identities I know.

]]>let be the n roots of unity. For which n and m does it hold that:

?]]>

can be generalized. For each integer , divides the determinant of a matrix in which each positive integer less than and coprime with appears exactly once in each row and in each column.

Yea I realized that when trying to sleep yesterday

edit: you dont need exactly once in the columns also

#13 is false for p=2.

true, forgot about that. Fixed!

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