For a string of length L, I want to find the longest substring that appears n (n<L) or more times in ths string.

For example, the longest substring that occurs 2 or more times in "BANANA" is "ANA", once starting from index 1, and once again starting from index 3. The substrings are allowed to overlap.

In the string "FFFFFF", the longest string that appears 3 or more times is "FFFF".

The brute force algorithm for n=2 would be selecting all pairs of indexes in the string, then running along until the characters are different. The running-along part takes O(L) and the number of pairs is O(L^2) (duplicates are not allowed but I'm ignoring that) so the complexity of this algorithm for n=2 would be O(L^3). For greater values of n, this grows exponentially.

Is there a more efficient algorithm for this problem?