Solution of the knight’s Hamiltonian path problem on chessboards

Is it possible for a knight to visit all squares of an n×n chessboard on an admissible path exactly once? The answer is yes if and only if n≥5. The kth position in such a path can be computed with a constant number of arithmetic operations. A Hamiltonian path from a given source s to a given terminal t exists for n≥6 if and only if some easily testable color criterion is fulfilled. Hamiltonian circuits exist if and only if n≥6 and n is even.