for q in [2..1000] do
    if not IsPrimePower(q) then
        continue;
    end if;
    fq:=GF(q);
    solutions:={x: x in (Set(fq) diff {0}) | ((x)^(-1)+(x)) eq 0};
    if #solutions gt 0 then
        print q, #solutions, solutions;
    end if;
end for;