Let r, n be positive integers with n≥6r. Let P be a polynomial of degree at most n on [0,1] with real coefficients, such that [formula] and [formula] are integers for k= 0,. . . , r − 1. It is proved that there is a polynomial Q of degree at most n with integer coefficients such that [formula] for x ∈ [0,1], where C1, C2 are some numerical constants. The result is the best possible up to the constants.