A function f:N→N, where N is the set of positive integers, satisfies the following condition: for any positive integers m and n (m>n) the number f(m)−f(n) is divisible by m−n.
Is the function f necessarily a polynomial? (In other words, is it true that for any such function there exists a polynomial p(x) with real coefficients such that f(n)=p(n) for all positive integers n?)(Folklore) number theoryfunctionalgebrapolynomial