Completing partial Latin squares with one filled row, column and symbol

Let P be an n × n partial Latin square every non-empty cell of which lies in a fixed row r, a fixed column c or contains a fixed symbol s. Assume further that s is the symbol of cell (r, c) in P . We prove that P is completable to a Latin square if n ≥ 8 and n is divisible by 4, or n ≤ 7 and n / ∈ {3, 4, 5}. Moreover, we present a polynomial algorithm for the completion of such a partial Latin square.