For every positive integer n, consider all monic polynomials f(x) with integer coefficients, such that for some real number a
x(f(x+a)−f(x))=nf(x)
Find the largest possible number of such polynomials f(x) for a fixed n<1000.
x(f(x+a)−f(x))=nf(x)
Find the largest possible number of such polynomials f(x) for a fixed n<1000.