You have $n$ congruent sticks (they have the same length). You want to divide them equaly among $m$ friends. To avoid envy, each friend should receive congruent parts, that is, the set of cutted sticks of one friend is exactly the same of any other friend.
Questions: Which is the minimal number of cuts in terms of $n$ and $m$? Is there an algorithm to decide where to cut?
Without the congruence restriction on the received cutted sticks, the problem was solved here.