conjcl := proc(k, p, n) local q, L, t, l; q := p^n - 1; L := [k]; t := 1; while (k*p^t - k) mod q <> 0 do L := [op(L), irem(k*p^t, q)]; t := t + 1; end do; return L; end proc

Figured it out since you told me about mod not distributing, ty so much!

@Carl Love Not sure if this helps, however here's the example output the professor gave us, as well as a remark on how to do it.I neednhe code to run until kp^m=k mod q, then append the value of kp^m in the list